منابع مشابه
On pancyclism in hamiltonian graphs
We investigate the set of cycle lengths occurring in a hamiltonian graph with at least one or two vertices of large degree. We prove that in every case this set contains all the integers between 3 and some t, where t depends on the order of the graph and the degrees of vertices. c © 2002 Elsevier Science B.V. All rights reserved.
متن کاملPancyclism and small cycles in graphs
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 ...
متن کاملHamiltonian Factors in Hamiltonian Graphs
Let G be a Hamiltonian graph. A factor F of G is called a Hamiltonian factor if F contains a Hamiltonian cycle. In this paper, two sufficient conditions are given, which are two neighborhood conditions for a Hamiltonian graph G to have a Hamiltonian factor. Keywords—graph, neighborhood, factor, Hamiltonian factor.
متن کاملA note on pancyclism of highly connected graphs
Jackson and Ordaz conjectured that if the stability number (G) of a graph G is no greater than its connectivity (G) then G is pancyclic. Applying Ramsey’s theorem we prove the pancyclicity of every graph G with (G) su7ciently large with respect to (G). c © 2003 Elsevier B.V. All rights reserved. MSC: 05C38; 05C45
متن کاملLong Cycles in Hamiltonian Graphs
We prove that if an n-vertex graph with minimum degree at least 3 contains a Hamiltonian cycle, then it contains another cycle of length n− o(n); in particular, this verifies, in an asymptotic form, a well-known conjecture due to Sheehan from 1975.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90361-5