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Tytuł:
The crossing numbers of join products of four graphs of order five with paths and cycles
Autorzy:
Staš, Michal
Timková, Mária
Powiązania:
https://bibliotekanauki.pl/articles/29519472.pdf
Data publikacji:
2023
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
graph
crossing number
join product
path
cycle
separating cycle
Opis:
The crossing number $ \text{cr} (G) $ of a graph $ G $ is the minimum number of edge crossings over all drawings of $ G $ in the plane. In the paper, we extend known results concerning crossing numbers of join products of four small graphs with paths and cycles. The crossing numbers of the join products $ G^∗ + P_n $ and $ G^∗ + C_n $ for the disconnected graph $ G^∗ $ consisting of the complete tripartite graph $ K_{1,1,2} $ and one isolated vertex are given, where $ P_n $ and $ C_n $ are the path and the cycle on $ n $ vertices, respectively. In the paper also the crossing numbers of $ H^∗ + P_n $ and $ H^∗ + C_n $ are determined, where $ H^∗ $ is isomorphic to the complete tripartite graph $ K_{1,1,3} $. Finally, by adding new edges to the graphs $ G^∗ $ and $ H^∗ $, we are able to obtain crossing numbers of join products of two other graphs $ G_1 $ and $ H_1 $ with paths and cycles.
Źródło:
Opuscula Mathematica; 2023, 43, 6; 865-883
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Decompositions of Complete Bipartite Graphs and Complete Graphs Into Paths, Stars, and Cycles with Four Edges Each
Autorzy:
Shyu, Tay-Woei
Powiązania:
https://bibliotekanauki.pl/articles/32083883.pdf
Data publikacji:
2021-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
complete graph
complete bipartite graph
path
star
cycle
decomposition
Opis:
Let G be either a complete graph of odd order or a complete bipartite graph in which each vertex partition has an even number of vertices. In this paper, we determine the set of triples (p, q, r), with p, q, r > 0, for which there exists a decomposition of G into p paths, q stars, and r cycles, each of which has 4 edges.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 2; 451-468
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Independent cycles and paths in bipartite balanced graphs
Autorzy:
Orchel, Beata
Wojda, A.
Powiązania:
https://bibliotekanauki.pl/articles/743087.pdf
Data publikacji:
2008
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
bipartite graphs
bi-placing
path
cycle
Opis:
Bipartite graphs G = (L,R;E) and H = (L',R';E') are bi-placeabe if there is a bijection f:L∪R→ L'∪R' such that f(L) = L' and f(u)f(v) ∉ E' for every edge uv ∈ E. We prove that if G and H are two bipartite balanced graphs of order |G| = |H| = 2p ≥ 4 such that the sizes of G and H satisfy ||G|| ≤ 2p-3 and ||H|| ≤ 2p-2, and the maximum degree of H is at most 2, then G and H are bi-placeable, unless G and H is one of easily recognizable couples of graphs. This result implies easily that for integers p and k₁,k₂,...,kₗ such that $k_i ≥ 2$ for i = 1,...,l and k₁ +...+ kₗ ≤ p-1 every bipartite balanced graph G of order 2p and size at least p²-2p+3 contains mutually vertex disjoint cycles $C_{2k₁},...,C_{2kₗ}$, unless $G = K_{3,3} - 3K_{1,1}$.
Źródło:
Discussiones Mathematicae Graph Theory; 2008, 28, 3; 535-549
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Transport rowerowy w Niemczech w latach dwudziestych i trzydziestych XX wieku
Bicycle transport in Germany in the 1920s and 1930s
Autorzy:
Mielcarek, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/28407381.pdf
Data publikacji:
2023
Wydawca:
Stowarzyszenie Inżynierów i Techników Komunikacji Rzeczpospolitej Polskiej
Tematy:
transport rowerowy
Niemcy w latach 20 i 30
ruch rowerowy
drogi dla rowerów
bicycle transport
Germany in the 1920s and 1930s
cycling
cycle paths
Opis:
W Niemczech rowery były najbardziej rozpowszechnionym środkiem transportu indywidualnego codziennego użytku. Służyły m.in. dojazdom do pracy i szkół. W latach 20. co piąty, a pod koniec lat 30. co trzeci mieszkaniec Niemiec był użytkownikiem roweru. Wobec rozwoju motoryzacji nastąpił konflikt między ruchem samochodowym i rowerowym. Rozwiązać go miała budowa dróg dla rowerów. W pierwszej części artykułu pokazano wyniki badań ruchu rowerowego w dni robocze i niedziele (latem) w latach 1936–1937. Badania przeprowadzono w związku z programem budowy dróg dla rowerów w miastach i poza nimi. Następnie przedstawiono dane o długości dróg rowerowych w Niemczech i we wschodnich prowincjach Niemiec, a także charakterystykę dróg rowerowych wybranych gmin miejskich wschodnich prowincji.
In Germany, bicycles were the most widespread means of individual daily transport, i.e. commuting to work, schools etc. In the 1920s one in five and by the end of the 1930s one in three Germans was a bicycle user. The development of automobile transport led to a conflict between car traffic and cyclists. It was to be solved by the construction of cycle paths. The first part of the article shows the results of a study on cycling traffic on (summer) weekdays and Sundays in the years 1936-37. The study was carried out in connection with a programme for the construction of cycle paths in and outside cities. This is followed by data on the length of cycle routes in Germany and the eastern provinces of Germany, as well as the characteristics of cycle routes in selected urban municipalities of the eastern provinces.
Źródło:
Transport Miejski i Regionalny; 2023, 4; 23--27
1732-5153
Pojawia się w:
Transport Miejski i Regionalny
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Decomposing the Complete Graph Into Hamiltonian Paths (Cycles) and 3-Stars
Autorzy:
Lee, Hung-Chih
Chen, Zhen-Chun
Powiązania:
https://bibliotekanauki.pl/articles/31521539.pdf
Data publikacji:
2020-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
decomposition
complete graph
Hamiltonian path
Hamiltonian cycle
star
Opis:
Let H be a graph. A decomposition of H is a set of edge-disjoint subgraphs of H whose union is H. A Hamiltonian path (respectively, cycle) of H is a path (respectively, cycle) that contains every vertex of H exactly once. A k-star, denoted by Sk, is a star with k edges. In this paper, we give necessary and sufficient conditions for decomposing the complete graph into α copies of Hamiltonian path (cycle) and β copies of S3.
Źródło:
Discussiones Mathematicae Graph Theory; 2020, 40, 3; 823-839
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The relationship between bicycle traffic and the development of bicycle infrastructure on the example of Warsaw
Autorzy:
Krukowicz, Tomasz
Firląg, Krzysztof
Sobota, Aleksander
Kołodziej, Tomasz
Novačko, Luka
Powiązania:
https://bibliotekanauki.pl/articles/2067411.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
bicycle
cycle paths
bicycle infrastructure
sustainable transport
vulnerable road user
Warsaw
rower
ścieżka rowerowa
infrastruktura rowerowa
transport zrównoważony
użytkownik dróg
Warszawa
Opis:
The article presents the relationship between the intensity of bicycle traffic volume and the development of bicycle infrastructure on the example of Warsaw. There has been a big increase in cycling over the last decade. At the same time, the linear and point bicycle infrastructure developed very strongly. Similar trends are also observed in other cities in Poland. The article presents the types of infrastructure available to cyclists. Then, the method of assessing the bicycle infrastructure is presented, taking into account the five features of good bicycle infrastructure: cohesion, directness, attractiveness, safety and comfort. In terms of coherence, the analysis covered the bicycle infrastructure network in the vicinity of the measurement site. The directness was tested by checking the accessibility of several dozen of the most important nodal points of the city's communication network. The attractiveness was examined by checking the availability of public bike stations, bicycle racks and bike-sharing stations. The infrastructure adjusted to the technical class of the road was adopted as a measure of safety. The comfort was checked by analyzing the quality of the road surface, which affects the driving comfort and energy expenditure. All the factors presented impact the cyclist's assessment of the infrastructure. To standardize the assessment rules, an aggregate index of the development of bicycle infrastructure was determined. The analysis was carried out for 10 sample points for four consecutive years. The points were characterized by different bicycle infrastructure, location in the city road network and different results of bicycle traffic measurements. The analysis showed a strong positive relationship between traffic and cycling infrastructure for most of the analyzed places. There was a negative dependence in the case of the construction of alternative routes in relation to the place of traffic measurements. The obtained results are the same as in the works of other authors. However, the effects of work do not allow to determine which of the examined factors is the cause and which is the effect but only show the existing relationship.
Źródło:
Archives of Transport; 2021, 60, 4; 187--203
0866-9546
2300-8830
Pojawia się w:
Archives of Transport
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The crossing numbers of products of a 5-vertex graph with paths and cycles
Autorzy:
Klešč, Marián
Powiązania:
https://bibliotekanauki.pl/articles/744243.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
drawing
crossing number
path
cycle
Cartesian product
Opis:
There are several known exact results on the crossing numbers of Cartesian products of paths, cycles or stars with "small" graphs. Let H be the 5-vertex graph defined from K₅ by removing three edges incident with a common vertex. In this paper, we extend the earlier results to the Cartesian products of H × Pₙ and H × Cₙ, showing that in the general case the corresponding crossing numbers are 3n-1, and 3n for even n or 3n+1 if n is odd.
Źródło:
Discussiones Mathematicae Graph Theory; 1999, 19, 1; 59-69
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Decomposition of Complete Bipartite Multigraphs Into Paths and Cycles Having $k$ Edges
Autorzy:
Jeevadoss, Shanmugasundaram
Muthusamy, Appu
Powiązania:
https://bibliotekanauki.pl/articles/31234097.pdf
Data publikacji:
2015-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
path
cycle
graph decomposition
multigraph
Opis:
We give necessary and sufficient conditions for the decomposition of complete bipartite multigraph $ K_{m,n} ( \lambda )$ into paths and cycles having $k$ edges. In particular, we show that such decomposition exists in $ K_{m,n} ( \lambda )$, when $ \lambda \equiv 0 (mod 2) $, $ m,n \geq k/2, m+n > k $ and $ k(p + q) = 2mn $ for $ k \equiv 0 (mod 2) $ and also when $ \lambda \geq 3 $, $ \lambda m \equiv \lambda n \equiv 0(mod 2) $, $ k(p + q) =\lambda m n $, $m, n \geq k $, (resp., $ m, n \geq 3k//2$) for $ k \equiv 0(mod 4)$ (respectively, for $ k \equiv 2(mod 4)$). In fact, the necessary conditions given above are also sufficient when $ \lambda = 2 $.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 4; 715-731
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Euro Velo. Sieć europejskich dróg rowerowych na terenie Polski
EuroVelo. The European cycle route network in Poland
Autorzy:
Goch, K.
Malasek, J.
Powiązania:
https://bibliotekanauki.pl/articles/192706.pdf
Data publikacji:
2013
Wydawca:
Stowarzyszenie Inżynierów i Techników Komunikacji Rzeczpospolitej Polskiej
Tematy:
EuroVelo
ruch rowerowy
trasy rowerowe
bicycle traffic
bike paths
Opis:
W ciągu ostatnich lat zaobserwowano wzrost popularności roweru jako środka transportu. Co najbardziej istotne, trend ten można zaobserwować nie tylko w małych miejscowościach, ale również w miastach i większych aglomeracjach. Rower zaczął być wykorzystywany jako środek transportu w trakcie codziennych podróży (do pracy, do szkoły, po zakupy). Ponadto wykorzystywanie roweru wpisało się w panującą modę na ekologiczny tryb życia. Rower to najbardziej przyjazny środowisku środek transportu, a jazda rowerem jest znakomitym sposobem rekreacji. Nie tylko młodzież, ale i osoby starsze wykorzystują rower do spędzania wolnego czasu w trakcie wycieczek po terenach zamiejskich. Centralna oraz lokalna administracja powinna wyjść naprzeciw oczekiwaniom i potrzebom związanym ze wzrostem ruchu rowerowego. Koordynatorzy krajowi EuroVelo w Polsce zostali powołani 11 października 2011 roku przez Radę EuroVelo. Na terenie Polski wytyczona jest sieć szlaków rowerowych o łącznej długości około 2000 kilometrów. Rozbudowa krajowej sieci tras rowerowych powinna nastąpić jak najszybciej, w celu zwiększenia turystycznej atrakcyjności Polski oraz podwyższenia udziału rowerów w podziale zadań przewozowych, co jest jednym z głównych celów polityki rozwoju zrównoważonego transportu. W poniższym artykule została opisana europejska sieć tras rowerowych EuroVelo, podstawowe wymagania dla dróg rowerowych oraz zamieszczono zdjęcia pokazujące przykłady optymalnych rozwiązań przyjaznej infrastruktury rowerowej. W tekście wykorzystano efekty udziału autorów artykułu w realizacji europejskiego projektu badawczego Step-by-Step i współpracy w ramach Grupy Roboczej JTRC „Cycling Safety Working Group”.
During last years high increase of cycling popularity in Poland has been observed. The most important is that people use more often bicycle as a travel mode for different purpose’s trips (to work, school, for shopping) not only in villages but also in the cities and big agglomerations. Nowadays cycling is fashionable – as environmental friendly and healthy way of recreation – and now not only young generation uses bicycles for long countryside journeys. Central as well as local administrations have to meet those needs. Polish National Coordinators were appointed by the EuroVelo Council in October 2011, what should be followed with a quick construction or upgrading of ca. 2000 kilometres long Polish sections of the European cycle route network. This will increase attractiveness of Poland among tourists and help in increase of a bicycle share in the modal split – fulfilling one of the sustainable urban transport policy goals. The paper below describes EuroVelo network, general design standards and presented pictures show how to organize a user friendly cycling infrastructure.
Źródło:
Transport Miejski i Regionalny; 2013, 9; 4-8
1732-5153
Pojawia się w:
Transport Miejski i Regionalny
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
$ \gamma $-Cycles In Arc-Colored Digraphs
Autorzy:
Galeana-Sánchez, Hortensia
Gaytán-Gómez, Guadalupe
Rojas-Monroy, Rocío
Powiązania:
https://bibliotekanauki.pl/articles/31341163.pdf
Data publikacji:
2016-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
digraph
kernel
kernel by monochromatic paths
γ-cycle
Opis:
We call a digraph $D$ an $m$-colored digraph if the arcs of $D$ are colored with $m$ colors. A directed path (or a directed cycle) is called monochromatic if all of its arcs are colored alike. A subdigraph $H$ in $D$ is called rainbow if all of its arcs have different colors. A set $ N \subseteq V (D) $ is said to be a kernel by monochromatic paths of $D$ if it satisfies the two following conditions: (i) for every pair of different vertices $ u, v \in N $ there is no monochromatic path in $D$ between them, and (ii) for every vertex $ x \in V (D) − N $ there is a vertex $ y \in N $ such that there is an $xy$-monochromatic path in $D$. A $\gamma$-cycle in $D$ is a sequence of different vertices $ \gamma = (u_0, u_1, . . ., u_n, u_0)$ such that for every $ i \in {0, 1, . . ., n}$: (i) there is a $u_i u_{i+1}$-monochromatic path, and (ii) there is no $u_{i+1}u_i$-monochromatic path. The addition over the indices of the vertices of $ \gamma $ is taken modulo $(n + 1)$. If $D$ is an $m$-colored digraph, then the closure of $D$, denoted by $ \mathfrak{C}(D)$, is the $m$-colored multidigraph defined as follows: $ V (\mathfrak{C} (D)) = V (D) $, $ A( \mathfrak{C} (D)) = A(D) \cup \{ (u, v) $ with color $i$ | there exists a $uv$-monochromatic path colored $i$ contained in $D \} $. In this work, we prove the following result. Let $D$ be a finite m-colored digraph which satisfies that there is a partition $ C = C_1 \cup C_2 $ of the set of colors of $D$ such that: (1) $ D[ \hat{C}_i ] $ (the subdigraph spanned by the arcs with colors in $ C_i) $ contains no $ \gamma $-cycles for $ i \in {1, 2} $; (2) If $ \mathfrak{C}(D) $ contains a rainbow $ C_3 = (x_0, z, w, x_0) $ involving colors of $ C_1 $ and $ C_2 $, then $ (x_0, w) \in A(\mathfrak{C} (D)) $ or $ (z, x_0) \in A( \mathfrak{C} (D)) $; (3) If $ \mathfrak{C}(D) $ contains a rainbow $ P_3 = (u, z, w, x_0) $ involving colors of $ C_1 $ and $ C_2 $, then at least one of the following pairs of vertices is an arc in $ \mathfrak{C} (D) $: $ (u, w) $, $ (w, u) $, $ (x_0, u) $, $ (u, x_0) $, $ (x_0, w) $, $ (z, u) $, $ (z, x_0) $. Then $D$ has a kernel by monochromatic paths. This theorem can be applied to all those digraphs that contain no $ \gamma $-cycles. Generalizations of many previous results are obtained as a direct consequence of this theorem.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 1; 103-116
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Monochromatic paths and monochromatic sets of arcs in 3-quasitransitive digraphs
Autorzy:
Galeana-Sánchez, Hortensia
Rojas-Monroy, R.
Zavala, B.
Powiązania:
https://bibliotekanauki.pl/articles/744398.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
m-coloured digraph
3-quasitransitive digraph
kernel by monochromatic paths
γ-cycle
quasi-monochromatic digraph
Opis:
We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path is called monochromatic if all of its arcs are coloured alike. A set N of vertices of D is called a kernel by monochromatic paths if for every pair of vertices of N there is no monochromatic path between them and for every vertex v ∉ N there is a monochromatic path from v to N. We denote by A⁺(u) the set of arcs of D that have u as the initial vertex. We prove that if D is an m-coloured 3-quasitransitive digraph such that for every vertex u of D, A⁺(u) is monochromatic and D satisfies some colouring conditions over one subdigraph of D of order 3 and two subdigraphs of D of order 4, then D has a kernel by monochromatic paths.
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 2; 337-347
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Longer-Term Demographic Dynamics in South-East Europe: Convergent, Divergent and Delayed Development Paths
Autorzy:
Fassmann, Heinz
Musil, Elisabeth
Bauer, Ramon
Melegh, Attila
Gruber, Kathrin
Powiązania:
https://bibliotekanauki.pl/articles/498627.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
demographic change
migration cycle
transitions
South-East Europe
Opis:
This article offers an overview of the longer-term migratory and demographic developments in eight South-East European countries (Austria, Bulgaria, Italy, Hungary, Romania, Serbia, Slovenia and Slovakia). The main research question aims to analyse the different demographic historical developments and to examine whether convergent or divergent processes are dominant. Over the whole reference period, the population size in these eight South-East European countries (the SEEMIG region) grew from around 100 million people in 1950 to 122 million in 2011. This is surprising, as the public image of the region is linked to decline and backwardness and to being peripheral. However, major differences in the demographic developments of the countries can be observed. Some countries, including Austria, Italy and, with some fluctuations, Slovakia and Slovenia, experienced constant population growth during the entire reference period. All other countries were affected by a decrease in population, as was the case for Hungary in the early 1980s, Bulgaria at the beginning of the 1990s and Serbia and Romania since the start of the new millennium. The fertility trend shows a convergence while the mortality trends (including average life expectancy at birth) prove to be divergent. The net migration pattern seems to follow a migration cycle concept which postulates a general shift from emigration to immigration as a consequence of a declining natural increase on the one hand and a growing demand for new labour on the other. Some countries show trends that do not yet follow this pattern, which might indicate that additional factors and interpretative models should also be taken into account. The long-term distribution of growth and decline in the region is quite diverse and underlines the need for differentiation and specific explanations.
Źródło:
Central and Eastern European Migration Review; 2014, 3, 2; 150-172
2300-1682
Pojawia się w:
Central and Eastern European Migration Review
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
γ-Cycles And Transitivity By Monochromatic Paths In Arc-Coloured Digraphs
Autorzy:
Casas-Bautista, Enrique
Galeana-Sánchez, Hortensia
Rojas-Monroy, Rocío
Powiązania:
https://bibliotekanauki.pl/articles/30146505.pdf
Data publikacji:
2013-07-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
digraph
kernel
kernel by monochromatic paths
γ-cycle
Opis:
We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. If D is an m-coloured digraph and a ∈ A(D), colour(a) will denote the colour has been used on a. A path (or a cycle) is called monochromatic if all of its arcs are coloured alike. A γ-cycle in D is a sequence of vertices, say γ = (u0, u1, . . ., un), such that ui ≠ uj if i ≠ j and for every i ∈ {0, 1, . . ., n} there is a uiui+1-monochromatic path in D and there is no ui+1ui-monochromatic path in D (the indices of the vertices will be taken mod n+1). A set N ⊆ V (D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) for every pair of different vertices u, v ∈ N there is no monochromatic path between them and; (ii) for every vertex x ∈ V (D) \ N there is a vertex y ∈ N such that there is an xy-monochromatic path. Let D be a finite m-coloured digraph. Suppose that {C1,C2} is a partition of C, the set of colours of D, and Di will be the spanning subdigraph of D such that A(Di) = {a ∈ A(D) | colour(a) ∈ Ci}. In this paper, we give some sufficient conditions for the existence of a kernel by monochromatic paths in a digraph with the structure mentioned above. In particular we obtain an extension of the original result by B. Sands, N. Sauer and R. Woodrow that asserts: Every 2-coloured digraph has a kernel by monochromatic paths. Also, we extend other results obtained before where it is proved that under some conditions an m-coloured digraph has no γ-cycles.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 3; 493-507
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On-line ranking number for cycles and paths
Autorzy:
Bruoth, Erik
Horňák, Mirko
Powiązania:
https://bibliotekanauki.pl/articles/744150.pdf
Data publikacji:
1999
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
ranking number
on-line vertex colouring
cycle
path
Opis:
A k-ranking of a graph G is a colouring φ:V(G) → {1,...,k} such that any path in G with endvertices x,y fulfilling φ(x) = φ(y) contains an internal vertex z with φ(z) > φ(x). On-line ranking number $χ*_r(G)$ of a graph G is a minimum k such that G has a k-ranking constructed step by step if vertices of G are coming and coloured one by one in an arbitrary order; when colouring a vertex, only edges between already present vertices are known. Schiermeyer, Tuza and Voigt proved that $χ*_r(Pₙ) < 3log₂n$ for n ≥ 2. Here we show that $χ*_r(Pₙ) ≤ 2⎣log₂n⎦+1$. The same upper bound is obtained for $χ*_r(Cₙ)$,n ≥ 3.
Źródło:
Discussiones Mathematicae Graph Theory; 1999, 19, 2; 175-197
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Multicolor Ramsey numbers for some paths and cycles
Autorzy:
Bielak, Halina
Powiązania:
https://bibliotekanauki.pl/articles/743153.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cycle
path
Ramsey number
Opis:
We give the multicolor Ramsey number for some graphs with a path or a cycle in the given sequence, generalizing a results of Faudree and Schelp [4], and Dzido, Kubale and Piwakowski [2,3].
Źródło:
Discussiones Mathematicae Graph Theory; 2009, 29, 2; 209-218
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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