Results 51 to 60 of about 998 (73)
On the Number of Disjoint 4-Cycles in Regular Tournaments
Discussiones Mathematicae Graph Theory, 2018 In this paper, we prove that for an integer r ≥ 1, every regular tournament T of degree 3r − 1 contains at least 2116r-103${{21} \over {16}}r - {{10} \over 3}$ disjoint directed 4-cycles. Our result is an improvement of Lichiardopol’s theorem when taking
Ma Fuhong, Yan Jin
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Forbidden Pairs and (k,m)-Pancyclicity
Discussiones Mathematicae Graph Theory, 2017 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}.
Crane Charles Brian
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On the n-Partite Tournaments with Exactly n − m + 1 Cycles of Length m
Discussiones Mathematicae Graph Theory, 2021 Gutin and Rafiey [Multipartite tournaments with small number of cycles, Australas J. Combin. 34 (2006) 17–21] raised the following two problems: (1) Let m ∈ {3, 4, . . ., n}.
Guo Qiaoping, Meng Wei
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Removable Edges on a Hamilton Cycle or Outside a Cycle in a 4-Connected Graph
Discussiones Mathematicae Graph Theory, 2021 Let G be a 4-connected graph. We call an edge e of G removable if the following sequence of operations results in a 4-connected graph: delete e from G; if there are vertices with degree 3 in G− e, then for each (of the at most two) such vertex x, delete ...
Wu Jichang +3 more
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Heavy Subgraphs, Stability and Hamiltonicity
Discussiones Mathematicae Graph Theory, 2017 Let G be a graph. Adopting the terminology of Broersma et al. and Čada, respectively, we say that G is 2-heavy if every induced claw (K1,3) of G contains two end-vertices each one has degree at least |V (G)|/2; and G is o-heavy if every induced claw of G
Li Binlong, Ning Bo
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Some Results on the Independence Polynomial of Unicyclic Graphs
Discussiones Mathematicae Graph Theory, 2018 Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial I(G,x)=∑k=0ns(G,k)xk$I(G,x) = \sum\nolimits_{k = 0}^n {s\left({G,k} \right)x^k }$, where s(
Oboudi Mohammad Reza
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The Crossing Number of Join of the Generalized Petersen Graph P(3, 1) with Path and Cycle
Discussiones Mathematicae Graph Theory, 2018 There are only few results concerning the crossing numbers of join of some graphs. In this paper, the crossing numbers of join products for the generalized Petersen graph P(3, 1) with n isolated vertices as well as with the path Pn on n vertices and with
Ouyang Zhang Dong +2 more
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Depth and Stanley depth of the edge ideals of the powers of paths and cycles
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2019 Let k be a positive integer. We compute depth and Stanley depth of the quotient ring of the edge ideal associated to the kth power of a path on n vertices.
Iqbal Zahid, Ishaq Muhammad
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Lower bound for the size of maximal nontraceable graphs
, 2004 Let g(n) denote the minimum number of edges of a maximal nontraceable graph of order n. Dudek, Katona and Wojda (2003) showed that g(n)\geq\ceil{(3n-2)/2}-2 for n\geq 20 and g(n)\leq\ceil{(3n-2)/2} for n\geq 54 as well as for n\in I={22,23,30,31,38,39 ...
Frick, Marietjie, Singleton, Joy
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Hamilton cycles in almost distance-hereditary graphs
Open Mathematics, 2016 Let G be a graph on n ≥ 3 vertices. A graph G is almost distance-hereditary if each connected induced subgraph H of G has the property dH(x, y) ≤ dG(x, y) + 1 for any pair of vertices x, y ∈ V(H).
Chen Bing, Ning Bo
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