منابع مشابه
2-Factor hamiltonian graphs
The Heawood graph and K3;3 have the property that all of their 2-factors are Hamilton circuits. We call such graphs 2-factor hamiltonian. We prove that if G is a k-regular bipartite 2factor hamiltonian graph then either G is a circuit or k 1⁄4 3: Furthermore, we construct an infinite family of cubic bipartite 2-factor hamiltonian graphs based on the Heawood graph and K3;3 and conjecture that th...
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We show that every hamiltonian claw-free graph with a vertex x of degree d(x) ≥ 7 has a 2-factor consisting of exactly two cycles.
متن کاملHamiltonian cycles in n-factor-critical graphs
A graph G is said to be n-factor-critical if G − S has a 1-factor for any S ⊂V (G) with |S| = n. In this paper, we prove that if G is a 2-connected n-factor-critical graph of order p with 3(G)¿ 2 (p−n−1), then G is hamiltonian with some exceptions. To extend this theorem, we de6ne a (k; n)-factor-critical graph to be a graph G such that G − S has a k-factor for any S ⊂V (G) with |S| = n. We con...
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 کاملOn the Extremal Number of Edges in 2-Factor Hamiltonian Graphs
In this paper we consider the question of determining the maximum number of edges in a hamiltonian graph of order n that contains no 2-factor with more than one cycle, that is, 2-factor hamiltonian graphs. We obtain exact results for both bipartite graphs, and general graphs, and construct extremal graphs in each case. Mathematics Subject Classification (2000). Primary 05C45; Secondary 05C38.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2003
ISSN: 0095-8956
DOI: 10.1016/s0095-8956(02)00031-x