Results 81 to 90 of about 1,777 (160)
Cycles in Random Bipartite Graphs [PDF]
, 2013 In this paper we study cycles in random bipartite graph $G(n,n,p)$. We prove that if $p\gg n^{-2/3}$, then $G(n,n,p)$ a.a.s. satisfies the following. Every subgraph $G'\subset G(n,n,p)$ with more than $(1+o(1))n^2p/2$ edges contains a cycle of length $t$
Shang, Yilun
core
Pancyclicity in claw-free graphs
Discrete Mathematics, 2002 AbstractIn this paper, we present several conditions for K1,3-free graphs, which guarantee the graph is subpancyclic. In particular, we show that every K1,3-free graph with a minimum degree sum δ2>23n+1−4; every {K1,3,P7}-free graph with δ2⩾9; every {K1,3,Z4}-free graph with δ2⩾9; and every K1,3-free graph with maximum degree Δ, diam(G)
Florian Pfender, Ronald J. Gould
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An Ore-type condition for pancyclability
Discrete Mathematics, 1999 AbstractLet G be a graph of order n and S a subset of V(G). We define G to be S-pancyclable if for every integer l,3⩽l⩽|S|, there exists a cycle in G that contains exactly l vertices of S. We prove that if the degree sum in G of every pair of nonadjacent vertices of S is at least n, then G is either S-pancyclable or else n is even, S=V(G) and G=Kn/2,n ...
Hao Li +3 more
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Chorded k-pancyclic and weakly k-pancyclic graphs [PDF]
, 2022 Megan Cream, Ronald J. Gould
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Global cycle properties in graphs with large minimum clustering coefficient
, 2016 The clustering coefficient of a vertex in a graph is the proportion of neighbours of the vertex that are adjacent. The minimum clustering coefficient of a graph is the smallest clustering coefficient taken over all vertices.
Borchert, Adam +2 more
core
Journal of Combinatorial Theory, Series B, 1971 AbstractA graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of all lengths l, 3 ≤ l ≤ | V(G) |.Theorem. Let G be Hamiltonian and suppose that |E(G)| ≥ n24, where n = |V(G)|. Then G is either pancyclic or else is the complete bipartite graph Kn2,n2.As a corollary to this theorem it is shown that the Ore conditions for a ...
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A characterization of pancyclic complements of line graphs
Discrete Mathematics, 2005 AbstractWe characterize graphs G such that the complements of their line graphs are pancyclic.
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Cycle-pancyclism in bipartite tournaments I
Discussiones Mathematicae Graph Theory, 2004 Let T be a Hamiltonian multipartite tournament with n vertices and γ a Hamiltonian cycle of T. We prove that for every k ,4 ≤ k ≤ n+4 , there exists a cycle C of length l(C) ∈{ k − 3 ,k − 2 ,k − 1 ,k }, whose intersection with the arcs of γ is at least l(C) − 3. In some cases the result is best possible.
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Low independence number and Hamiltonicity implies pancyclicity [PDF]
, 2020 Attila Dankovics
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