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Wyświetlanie 1-15 z 19
Tytuł:
Application of Hamiltons graph theory in new technologies
Autorzy:
Waligóra, Łucja
Powiązania:
https://bibliotekanauki.pl/articles/1178878.pdf
Data publikacji:
2017
Wydawca:
Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
Tematy:
Hamilton cycle
IT tests
graphs
Opis:
There are many theories and articles about testing. People try to find the best ways to design computer systems for their later usability tests and functional tests. The article presents a somewhat mathematical approach to testing using graph theory and Hamilton's cycles. The inspiration for writing the article was the development of the text. Graphs as a decision support tool by Ewa Pospiech in the paper entitled " Elements of mathematics for economics and management students. Decisions, edited by J. Mika and A. Mastalerz – Kodzis.
Źródło:
World Scientific News; 2017, 89; 71-81
2392-2192
Pojawia się w:
World Scientific News
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hamilton Cycles in Double Generalized Petersen Graphs
Autorzy:
Sakamoto, Yutaro
Powiązania:
https://bibliotekanauki.pl/articles/31343695.pdf
Data publikacji:
2019-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
double generalized Petersen graph
Hamilton cycle
Opis:
Coxeter referred to generalizing the Petersen graph. Zhou and Feng modified the graphs and introduced the double generalized Petersen graphs (DGPGs). Kutnar and Petecki proved that DGPGs are Hamiltonian in special cases and conjectured that all DGPGs are Hamiltonian. In this paper, we prove the conjecture by constructing Hamilton cycles in any given DGPG.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 1; 117-123
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hamilton cycles in split graphs with large minimum degree
Autorzy:
Tan, Ngo
Hung, Le
Powiązania:
https://bibliotekanauki.pl/articles/744406.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Hamilton cycle
split graph
bipartite graph
Opis:
A graph G is called a split graph if the vertex-set V of G can be partitioned into two subsets V₁ and V₂ such that the subgraphs of G induced by V₁ and V₂ are empty and complete, respectively. In this paper, we characterize hamiltonian graphs in the class of split graphs with minimum degree δ at least |V₁| - 2.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 1; 23-40
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Fan-Type Heavy Pair Of Subgraphs For Pancyclicity Of 2-Connected Graphs
Autorzy:
Wideł, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/31341120.pdf
Data publikacji:
2016-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cycle
Fan-type heavy subgraph
Hamilton cycle
pancyclicity
Opis:
Let $G$ be a graph on $n$ vertices and let $H$ be a given graph. We say that $G$ is pancyclic, if it contains cycles of all lengths from 3 up to $n$, and that it is $H-f_1$-heavy, if for every induced subgraph $K$ of $G$ isomorphic to $H$ and every two vertices $u, v \in V (K)$, $d_K(u, v) = 2$ implies $ \text{min} \{ d_G(u), d_G(v) \} \ge \frac{n+1}{2} $. In this paper we prove that every 2-connected $ \{ K_{1,3} , P_5}-f_1$-heavy graph is pancyclic. This result completes the answer to the problem of finding $ f_1 $-heavy pairs of subgraphs implying pancyclicity of 2-connected graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 1; 173-184
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs
Autorzy:
Wide, Wojciech
Powiązania:
https://bibliotekanauki.pl/articles/31341826.pdf
Data publikacji:
2017-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cycle
Fan-type heavy subgraph
Hamilton cycle
pancyclicity
Opis:
A graph G on n vertices is said to be pancyclic if it contains cycles of all lengths k for k ∈ {3, . . ., n}. A vertex v ∈ V (G) is called super-heavy if the number of its neighbours in G is at least (n+1)/2. For a given graph H we say that G is H-f1-heavy if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K), dK(u, v) = 2 implies that at least one of them is super-heavy. For a family of graphs ℋ we say that G is ℋ-f1-heavy, if G is H-f1-heavy for every graph H ∈ℋ. Let D denote the deer, a graph consisting of a triangle with two disjoint paths P3 adjoined to two of its vertices. In this paper we prove that every 2-connected {K1,3, P7, D}-f1-heavy graph on n ≥ 14 vertices is pancyclic. This result extends the previous work by Faudree, Ryjáček and Schiermeyer.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 2; 477-499
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Note on Barnette’s Conjecture
Autorzy:
Harant, Jochen
Powiązania:
https://bibliotekanauki.pl/articles/30146724.pdf
Data publikacji:
2013-03-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
planar graph
Hamilton cycle
Barnette’s Conjecture
Opis:
Barnette conjectured that each planar, bipartite, cubic, and 3-connected graph is hamiltonian. We prove that this conjecture is equivalent to the statement that there is a constant c > 0 such that each graph G of this class contains a path on at least c|V (G)| vertices.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 1; 133-137
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Edge condition for hamiltonicity in balanced tripartite graphs
Autorzy:
Adamus, J.
Powiązania:
https://bibliotekanauki.pl/articles/255875.pdf
Data publikacji:
2009
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Hamilton cycle
pancyclicity
tripartite graph
edge condition
Opis:
A well-known theorem of Entringer and Schmeichel asserts that a balanced bipartite graph of order 2n obtained from the complete balanced bipartite Kn,n by removing at most n - 2 edges, is bipancyclic. We prove an analogous result for balanced tripartite graphs: If G is a balanced tripartite graph of order 3n and size at least 3n(2) - 2n + 2, then G contains cycles of all lengths.
Źródło:
Opuscula Mathematica; 2009, 29, 4; 337-343
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords
Autorzy:
Affif Chaouche, Fatima
Rutherford, Carrie G.
Whitty, Robin W.
Powiązania:
https://bibliotekanauki.pl/articles/31339337.pdf
Data publikacji:
2015-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
extremal graph theory
pancyclic graph
Hamilton cycle
Opis:
It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required. A possibly ‘intermediate’ variation is the following: given k, 1 ≤ k ≤ n, how many chords must be added to ensure that there exist cycles of every possible length each of which passes exactly k chords? For fixed k, we establish a lower bound of Ω(n1/k) on the growth rate.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 3; 533-539
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Families of triples with high minimum degree are Hamiltonian
Autorzy:
Rödl, Vojtech
Ruciński, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/30148238.pdf
Data publikacji:
2014-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
3-uniform hypergraph
Hamilton cycle
minimum vertex degree
Opis:
In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least $$(\frac{5−√5}{3} + γ)\binom{n−1}{2}$$ contains a tight Hamiltonian cycle.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 2; 361-381
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Perfect Set of Euler Tours of Kp,p,p
Autorzy:
Govindan, T.
Muthusamy, A.
Powiązania:
https://bibliotekanauki.pl/articles/31340779.pdf
Data publikacji:
2016-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
compatible Euler tour
line graph
Hamilton cycle decomposition
Opis:
Bermond conjectured that if G is Hamilton cycle decomposable, then L(G), the line graph of G, is Hamilton cycle decomposable. In this paper, we construct a perfect set of Euler tours for the complete tripartite graph Kp,p,p for any prime p and hence prove Bermond’s conjecture for G = Kp,p,p.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 4; 783-796
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Symmetric Hamilton Cycle Decompositions of Complete Multigraphs
Autorzy:
Chitra, V.
Muthusamy, A.
Powiązania:
https://bibliotekanauki.pl/articles/29788703.pdf
Data publikacji:
2013-09-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
complete multigraph
1-factor
symmetric Hamilton cycle
decomposition
Opis:
Let $n ≥ 3$ and $⋋ ≥ 1$ be integers. Let $⋋K_n$ denote the complete multigraph with edge-multiplicity $⋋$. In this paper, we show that there exists a symmetric Hamilton cycle decomposition of $⋋K_{2m}$ for all even $⋋ ≥ 2$ and $m ≥ 2$. Also we show that there exists a symmetric Hamilton cycle decomposition of $⋋K_{2m} − F$ for all odd $⋋ ≥ 3$ and $m ≥ 2$. In fact, our results together with the earlier results (by Walecki and Brualdi and Schroeder) completely settle the existence of symmetric Hamilton cycle decomposition of $⋋K_n$ (respectively, $⋋K_n − F$, where $F$ is a 1-factor of $⋋K_n$) which exist if and only if $⋋(n − 1)$ is even (respectively, $⋋(n − 1)$ is odd), except the non-existence cases n ≡ 0 or 6 (mod 8) when ⋋ = 1
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 4; 695-707
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hamiltonicity and Generalised Total Colourings of Planar Graphs
Autorzy:
Borowiecki, Mieczysław
Broere, Izak
Powiązania:
https://bibliotekanauki.pl/articles/31341094.pdf
Data publikacji:
2016-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
even planar triangulation
total colouring
Hamilton cycle
hereditary property
Opis:
The total generalised colourings considered in this paper are colourings of graphs such that the vertices and edges of the graph which receive the same colour induce subgraphs from two prescribed hereditary graph properties while incident elements receive different colours. The associated total chromatic number is the least number of colours with which this is possible. We study such colourings for sets of planar graphs and determine, in particular, upper bounds for these chromatic numbers for proper colourings of the vertices while the monochromatic edge sets are allowed to be forests. We also prove that if an even planar triangulation has a Hamilton cycle H for which there is no cycle among the edges inside H, then such a graph needs at most four colours for a total colouring as described above. The paper is concluded with some conjectures and open problems.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 2; 243-257
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A σ₃ type condition for heavy cycles in weighted graphs
Autorzy:
Zhang, Shenggui
Li, Xueliang
Broersma, Hajo
Powiązania:
https://bibliotekanauki.pl/articles/743462.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
weighted graph
(long, heavy, Hamilton) cycle
weighted degree
(weighted) degree sum
Opis:
A weighted graph is a graph in which each edge e is assigned a non-negative number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges. The weighted degree $d^w(v)$ of a vertex v is the sum of the weights of the edges incident with v. In this paper, we prove the following result: Suppose G is a 2-connected weighted graph which satisfies the following conditions: 1. The weighted degree sum of any three independent vertices is at least m; 2. w(xz) = w(yz) for every vertex z ∈ N(x)∩N(y) with d(x,y) = 2; 3. In every triangle T of G, either all edges of T have different weights or all edges of T have the same weight. Then G contains either a Hamilton cycle or a cycle of weight at least 2m/3. This generalizes a theorem of Fournier and Fraisse on the existence of long cycles in k-connected unweighted graphs in the case k = 2. Our proof of the above result also suggests a new proof to the theorem of Fournier and Fraisse in the case k = 2.
Źródło:
Discussiones Mathematicae Graph Theory; 2001, 21, 2; 159-166
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Heavy cycles in weighted graphs
Autorzy:
Bondy, J.
Broersma, Hajo
van den Heuvel, Jan
Veldman, Henk
Powiązania:
https://bibliotekanauki.pl/articles/743527.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
weighted graph
(long, optimal, Hamilton) cycle
(edge-, vertex-)weighting
weighted degree
Opis:
An (edge-)weighted graph is a graph in which each edge e is assigned a nonnegative real number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges, and an optimal cycle is one of maximum weight. The weighted degree w(v) of a vertex v is the sum of the weights of the edges incident with v. The following weighted analogue (and generalization) of a well-known result by Dirac for unweighted graphs is due to Bondy and Fan. Let G be a 2-connected weighted graph such that w(v) ≥ r for every vertex v of G. Then either G contains a cycle of weight at least 2r or every optimal cycle of G is a Hamilton cycle. We prove the following weighted analogue of a generalization of Dirac's result that was first proved by Pósa. Let G be a 2-connected weighted graph such that w(u)+w(v) ≥ s for every pair of nonadjacent vertices u and v. Then G contains either a cycle of weight at least s or a Hamilton cycle. Examples show that the second conclusion cannot be replaced by the stronger second conclusion from the result of Bondy and Fan. However, we characterize a natural class of edge-weightings for which these two conclusions are equivalent, and show that such edge-weightings can be recognized in time linear in the number of edges.
Źródło:
Discussiones Mathematicae Graph Theory; 2002, 22, 1; 7-15
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Implicit Heavy Subgraphs and Hamiltonicity of 2-Connected Graphs
Autorzy:
Zheng, Wei
Wideł, Wojciech
Wang, Ligong
Powiązania:
https://bibliotekanauki.pl/articles/32083821.pdf
Data publikacji:
2021-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
implicit degree
implicit o-heavy
implicit f-heavy
implicit c-heavy
Hamilton cycle
Opis:
A graph G of order n is implicit claw-heavy if in every induced copy of K1,3 in G there are two non-adjacent vertices with sum of their implicit degrees at least n. We study various implicit degree conditions (including, but not limiting to, Ore- and Fan-type conditions) imposing of which on specific induced subgraphs of a 2-connected implicit claw-heavy graph ensures its Hamiltonicity. In particular, we improve a recent result of [X. Huang, Implicit degree condition for Hamiltonicity of 2-heavy graphs, Discrete Appl. Math. 219 (2017) 126–131] and complete the characterizations of pairs of o-heavy and f-heavy subgraphs for Hamiltonicity of 2-connected graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 1; 167-181
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
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