Results 71 to 80 of about 1,777 (160)
Journal of Combinatorial Theory, Series B, 1976 Abstract A 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)| ≥ n 2 4 , where n = |V(G)|. Then G is either pancyclic or else is the complete bipartite graph K n 2 , n 2 .
J.A Bondy, A. W. Ingleton
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The Cycle Spectrum of Claw-free Hamiltonian Graphs [PDF]
, 2013 If $G$ is a claw-free hamiltonian graph of order $n$ and maximum degree $\Delta$ with $\Delta\geq 24$, then $G$ has cycles of at least $\min\left\{ n,\left\lceil\frac{3}{2}\Delta\right\rceil\right\}-2$ many different lengths.Comment: 9 ...
Eckert, Jonas +2 more
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On the vertex-pancyclicity of hypertournaments
Discrete Applied Mathematics, 2013 A k-hypertournament H on n vertices, where 2@?k@?n, is a pair H=(V,A"H), where V is the vertex set of H and A"H is a set of k-tuples of vertices, called arcs, such that, for all subsets S@?V with |S|=k, A"H contains exactly one permutation of S as an arc.
Hongwei Li +3 more
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An upper bound for the crossing number of augmented cubes [PDF]
, 2012 A {\it good drawing} of a graph $G$ is a drawing where the edges are non-self-intersecting and each two edges have at most one point in common, which is either a common end vertex or a crossing.
Wang, Guoqing +4 more
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A sufficient condition for pre-Hamiltonian cycles in bipartite digraphs
, 2017 Let $D$ be a strongly connected balanced bipartite directed graph of order $2a\geq 10$ other than a directed cycle. Let $x,y$ be distinct vertices in $D$.
Darbinyan, Samvel Kh. +1 more
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A sufficient condition for pancyclability of graphs
Discrete Mathematics, 2009 AbstractLet G be a graph of order n and S be a vertex set of q vertices. We call G,S-pancyclable, if for every integer i with 3≤i≤q there exists a cycle C in G such that |V(C)∩S|=i. For any two nonadjacent vertices u,v of S, we say that u,v are of distance two in S, denoted by dS(u,v)=2, if there is a path P in G connecting u and v such that |V(P)∩S|≤3.
Hao Li, Bing Wei, Evelyne Flandrin
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Pancyclism and Meyniel's conditions
Discrete Mathematics, 1986 AbstractWe prove that a strong digraph of order n and such that, for each pair of non adjacent vertices, the degree sum is at least 2n − 1, is pancyclic with some exceptions.
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On the pancyclicity of 1-tough graphs [PDF]
Discrete Mathematics Letters, 2020 Rao Li
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, 2013 We prove that every possible $k$-cycle can be embedded into $PG(n,q)$, for all $n\geq 3$ and $q$ a power of a prime.Comment: 6 ...
Aceves, Elaina +3 more
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Edge-Fault Tolerance of Hypercube-like Networks [PDF]
, 2012 This paper considers a kind of generalized measure $\lambda_s^{(h)}$ of fault tolerance in a hypercube-like graph $G_n$ which contain several well-known interconnection networks such as hypercubes, varietal hypercubes, twisted cubes, crossed cubes and M\"
Li, Xiang-Jun, Xu, Jun-Ming
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