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Wyświetlanie 1-15 z 23
Tytuł:
Pancyclism and small cycles in graphs
Autorzy:
Faudree, Ralph
Favaron, Odile
Flandrin, Evelynei
Li, Hao
Powiązania:
https://bibliotekanauki.pl/articles/972039.pdf
Data publikacji:
1996
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cycle
hamiltonian
pancyclic
Opis:
We first show that if a graph G of order n contains a hamiltonian path connecting two nonadjacent vertices u and v such that d(u)+d(v) ≥ n, then G is pancyclic. By using this result, we prove that if G is hamiltonian with order n ≥ 20 and if G has two nonadjacent vertices u and v such that d(u)+d(v) ≥ n+z, where z = 0 when n is odd and z = 1 otherwise, then G contains a cycle of length m for each 3 ≤ m ≤ max (d_C(u,v)+1, [(n+19)/13]), $d_C(u,v)$ being the distance of u and v on a hamiltonian cycle of G.
Źródło:
Discussiones Mathematicae Graph Theory; 1996, 16, 1; 27-40
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A note on maximal common subgraphs of the Diracs family of graphs
Autorzy:
Bucko, Jozef
Mihók, Peter
Saclé, Jean-François
Woźniak, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/744168.pdf
Data publikacji:
2005
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
maximal common subgraph
Dirac's family
Hamiltonian cycle
Opis:
Let ⁿ be a given set of unlabeled simple graphs of order n. A maximal common subgraph of the graphs of the set ⁿ is a common subgraph F of order n of each member of ⁿ, that is not properly contained in any larger common subgraph of each member of ⁿ. By well-known Dirac's Theorem, the Dirac's family ⁿ of the graphs of order n and minimum degree δ ≥ [n/2] has a maximal common subgraph containing Cₙ. In this note we study the problem of determining all maximal common subgraphs of the Dirac's family $ ^{2n}$ for n ≥ 2.
Źródło:
Discussiones Mathematicae Graph Theory; 2005, 25, 3; 385-390
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Chvátals Condition cannot hold for both a graph and its complement
Autorzy:
Kostochka, Alexandr
West, Douglas
Powiązania:
https://bibliotekanauki.pl/articles/743881.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Hamiltonian cycle
Chvátal's Condition
random graph
Opis:
Chvátal's Condition is a sufficient condition for a spanning cycle in an n-vertex graph. The condition is that when the vertex degrees are d₁, ...,dₙ in nondecreasing order, i < n/2 implies that $d_i > i$ or $d_{n-i} ≥ n-i$. We prove that this condition cannot hold in both a graph and its complement, and we raise the problem of finding its asymptotic probability in the random graph with edge probability 1/2.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 1; 73-76
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Chvátal-Erdős condition and 2-factors with a specified number of components
Autorzy:
Chen, Guantao
Gould, Ronald
Kawarabayashi, Ken-ichi
Ota, Katsuhiro
Saito, Akira
Schiermeyer, Ingo
Powiązania:
https://bibliotekanauki.pl/articles/743407.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Chvátal-Erdös condition
2-factor
hamiltonian cycle
Ramsey number
Opis:
Let G be a 2-connected graph of order n satisfying α(G) = a ≤ κ(G), where α(G) and κ(G) are the independence number and the connectivity of G, respectively, and let r(m,n) denote the Ramsey number. The well-known Chvátal-Erdös Theorem states that G has a hamiltonian cycle. In this paper, we extend this theorem, and prove that G has a 2-factor with a specified number of components if n is sufficiently large. More precisely, we prove that (1) if n ≥ k·r(a+4, a+1), then G has a 2-factor with k components, and (2) if n ≥ r(2a+3, a+1)+3(k-1), then G has a 2-factor with k components such that all components but one have order three.
Źródło:
Discussiones Mathematicae Graph Theory; 2007, 27, 3; 401-407
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On a family of cubic graphs containing the flower snarks
Autorzy:
Fouquet, Jean-Luc
Thuillier, Henri
Vanherpe, Jean-Marie
Powiązania:
https://bibliotekanauki.pl/articles/744266.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cubic graph
perfect matching
strong matching
counting
hamiltonian cycle
2-factor hamiltonian
Opis:
We consider cubic graphs formed with k ≥ 2 disjoint claws $C_i ~ K_{1,3}$ (0 ≤ i ≤ k-1) such that for every integer i modulo k the three vertices of degree 1 of $C_i$ are joined to the three vertices of degree 1 of $C_{i-1}$ and joined to the three vertices of degree 1 of $C_{i+1}$. Denote by $t_i$ the vertex of degree 3 of $C_i$ and by T the set ${t₁,t₂,...,t_{k-1}}$. In such a way we construct three distinct graphs, namely FS(1,k), FS(2,k) and FS(3,k). The graph FS(j,k) (j ∈ {1,2,3}) is the graph where the set of vertices $⋃_{i = 0}^{i = k-1} V(C_i)∖T$ induce j cycles (note that the graphs FS(2,2p+1), p ≥ 2, are the flower snarks defined by Isaacs [8]). We determine the number of perfect matchings of every FS(j,k). A cubic graph G is said to be 2-factor hamiltonian if every 2-factor of G is a hamiltonian cycle. We characterize the graphs FS(j,k) that are 2-factor hamiltonian (note that FS(1,3) is the "Triplex Graph" of Robertson, Seymour and Thomas [15]). A strong matching M in a graph G is a matching M such that there is no edge of E(G) connecting any two edges of M. A cubic graph having a perfect matching union of two strong matchings is said to be a Jaeger's graph. We characterize the graphs FS(j,k) that are Jaeger's graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2010, 30, 2; 289-314
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Research problems from the 18th Workshop '3in1' 2009
Autorzy:
Meszka, M. [ed.]
Powiązania:
https://bibliotekanauki.pl/articles/255619.pdf
Data publikacji:
2010
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Hamilton-connected graph
hamiltonian graph
dominating cycle
bihomogeneously traceble graph
Opis:
A collection of open problems that were posed at the 18th Workshop '3in1', held on November 26-28, 2009 in Krakow, Poland. The problems are presented by Zdenek Ryjacek in "Does the Thomassen's conjecture imply N=NP?" and "Dominating cycles and hamiltonian prisms", and by Carol T. Zamfirescu in "Two problems on bihomogeneously traceable digraphs".
Źródło:
Opuscula Mathematica; 2010, 30, 4; 527-532
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Vertices Enforcing a Hamiltonian Cycle
Autorzy:
Fabrici, Igor
Hexel, Erhard
Jendrol’, Stanislav
Powiązania:
https://bibliotekanauki.pl/articles/30146856.pdf
Data publikacji:
2013-03-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cycle
hamiltonian
1-hamiltonian
Opis:
A nonempty vertex set X ⊆ V (G) of a hamiltonian graph G is called an H-force set of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian. The H-force number h(G) of a graph G is defined to be the smallest cardinality of an H-force set of G. In the paper the study of this parameter is introduced and its value or a lower bound for outerplanar graphs, planar graphs, k-connected graphs and prisms over graphs is determined.
Źródło:
Discussiones Mathematicae Graph Theory; 2013, 33, 1; 71-89
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Uniquely Hamiltonian Claw-Free and Triangle-Free Graphs
Autorzy:
Seamone, Ben
Powiązania:
https://bibliotekanauki.pl/articles/31339495.pdf
Data publikacji:
2015-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Hamiltonian cycle
uniquely Hamiltonian graphs
claw-free graphs
triangle-free graphs
Opis:
A graph is uniquely Hamiltonian if it contains exactly one Hamiltonian cycle. In this note, we prove that claw-free graphs with minimum degree at least 3 are not uniquely Hamiltonian. We also show that this is best possible by exhibiting uniquely Hamiltonian claw-free graphs with minimum degree 2 and arbitrary maximum degree. Finally, we show that a construction due to Entringer and Swart can be modified to construct triangle-free uniquely Hamiltonian graphs with minimum degree 3.
Źródło:
Discussiones Mathematicae Graph Theory; 2015, 35, 2; 207-214
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fans condition on induced subgraphs for circumference and pancyclicity
Autorzy:
Wideł, W.
Powiązania:
https://bibliotekanauki.pl/articles/255831.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Fan's condition
circumference
hamiltonian cycle
pancyclicity
Opis:
Let H be a family of simple graphs and k be a positive integer. We say that a graph G of order n ≥ k satisfies Fan's condition with respect to H with constant k, if for every induced subgraph H of G isomorphic to any of the graphs from H the following holds: [formula] If G satisfies the above condition, we write [formula]. In this paper we show that if G is 2-connected and [formula], then G contains a cycle of length at least k, and that if [formula], then G is pancyclic with some exceptions. As corollaries we obtain the previous results by Fan, Benhocine and Wojda, and Ning.
Źródło:
Opuscula Mathematica; 2017, 37, 4; 617-639
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Forbidden Pairs and (k, m)-Pancyclicity
Autorzy:
Crane, Charles Brian
Powiązania:
https://bibliotekanauki.pl/articles/31341696.pdf
Data publikacji:
2017-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hamiltonian
pancyclic
forbidden subgraph
cycle
claw-free
Opis:
A graph G on n vertices is said to be (k,m)-pancyclic if every set of k vertices in G is contained in a cycle of length r for each r ∈ {m, m+1, . . ., n}. This property, which generalizes the notion of a vertex pancyclic graph, was defined by Faudree, Gould, Jacobson, and Lesniak in 2004. The notion of (k, m)-pancyclicity provides one way to measure the prevalence of cycles in a graph. We consider pairs of subgraphs that, when forbidden, guarantee hamiltonicity for 2-connected graphs on n ≥ 10 vertices. There are exactly ten such pairs. For each integer k ≥ 1 and each of eight such subgraph pairs {R, S}, we determine the smallest value m such that any 2-connected {R, S}-free graph on n ≥ 10 vertices is guaranteed to be (k,m)-pancyclic. Examples are provided that show the given values are best possible. Each such example we provide represents an infinite family of graphs.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 3; 649-663
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the H -Force Number of Hamiltonian Graphs and Cycle Extendability
Autorzy:
Hexel, Erhard
Powiązania:
https://bibliotekanauki.pl/articles/31342172.pdf
Data publikacji:
2017-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cycle
hamiltonian graph
H -force number
cycle extendability
Opis:
The H-force number h(G) of a hamiltonian graph G is the smallest cardinality of a set A ⊆ V (G) such that each cycle containing all vertices of A is hamiltonian. In this paper a lower and an upper bound of h(G) is given. Such graphs, for which h(G) assumes the lower bound are characterized by a cycle extendability property. The H-force number of hamiltonian graphs which are exactly 2-connected can be calculated by a decomposition formula.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 1; 79-88
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Arc-Disjoint Hamiltonian Cycles in Round Decomposable Locally Semicomplete Digraphs
Autorzy:
Li, Ruijuan
Han, Tingting
Powiązania:
https://bibliotekanauki.pl/articles/31342322.pdf
Data publikacji:
2018-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
locally semicomplete digraph
local tournament
round decomposable
arc-disjoint
Hamiltonian cycle
Hamiltonian path
Opis:
Let D = (V,A) be a digraph; if there is at least one arc between every pair of distinct vertices of D, then D is a semicomplete digraph. A digraph D is locally semicomplete if for every vertex x, the out-neighbours of x induce a semicomplete digraph and the in-neighbours of x induce a semicomplete digraph. A locally semicomplete digraph without 2-cycle is a local tournament. In 2012, Bang-Jensen and Huang [J. Combin Theory Ser. B 102 (2012) 701–714] concluded that every 2-arc-strong locally semicomplete digraph which is not the second power of an even cycle has two arc-disjoint strong spanning subdigraphs, and proposed the conjecture that every 3-strong local tournament has two arc-disjoint Hamiltonian cycles. According to Bang-Jensen, Guo, Gutin and Volkmann, locally semicomplete digraphs have three subclasses: the round decomposable; the non-round decomposable which are not semicomplete; the non-round decomposable which are semicomplete. In this paper, we prove that every 3-strong round decomposable locally semicomplete digraph has two arc-disjoint Hamiltonian cycles, which implies that the conjecture holds for the round decomposable local tournaments. Also, we characterize the 2-strong round decomposable local tournaments each of which contains a Hamiltonian path P and a Hamiltonian cycle arc-disjoint from P.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 2; 477-490
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Matchings Extend to Hamiltonian Cycles in 5-Cube
Autorzy:
Wang, Fan
Zhao, Weisheng
Powiązania:
https://bibliotekanauki.pl/articles/31342429.pdf
Data publikacji:
2018-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
hypercube
Hamiltonian cycle
matching
Opis:
Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture. Also, Fink pointed out that every matching can be extended to a Hamiltonian cycle of Qn for n ∈ {2, 3, 4}. In this paper, we prove that every matching in Q5 can be extended to a Hamiltonian cycle of Q5.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 1; 217-231
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Hamiltonian Normal Cayley Graphs
Autorzy:
Montellano-Ballesteros, Juan José
Arguello, Anahy Santiago
Powiązania:
https://bibliotekanauki.pl/articles/31343293.pdf
Data publikacji:
2019-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Cayley graph
hamiltonian cycle
normal connection set
Opis:
A variant of the Lovász Conjecture on hamiltonian paths states that every finite connected Cayley graph contains a hamiltonian cycle. Given a finite group G and a connection set S, the Cayley graph Cay(G, S) will be called normal if for every g ∈ G we have that g−1Sg = S. In this paper we present some conditions on the connection set of a normal Cayley graph which imply the existence of a hamiltonian cycle in the graph.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 3; 731-740
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Hamiltonian Number of a Plane Graph
Autorzy:
Lewis, Thomas M.
Powiązania:
https://bibliotekanauki.pl/articles/31343593.pdf
Data publikacji:
2019-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Hamiltonian cycle
Hamiltonian walk
Hamiltonian number
Hamiltonian spectrum
Grinberg’s theorem
planar graph
Opis:
The Hamiltonian number of a connected graph is the minimum of the lengths of the closed spanning walks in the graph. In 1968, Grinberg published a necessary condition for the existence of a Hamiltonian cycle in a plane graph, formulated in terms of the degrees of its faces. We show how Grinberg’s theorem can be adapted to provide a lower bound on the Hamiltonian number of a plane graph.
Źródło:
Discussiones Mathematicae Graph Theory; 2019, 39, 1; 171-181
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 23

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