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A k-HAMILTON-NICE SEQUENCE

Yiping Liu、Zhengsheng Wu

1992Computer Science被引 1

摘要

Let G be a simple finite graph, Ik+1 (G) the set of independent sets of cardinality (k + 1) of G. If Y ∈Ik+1(G), define Si(Y)={v|N(v) n Y| = i}, si(Y) =|Si(Y)|for each i ∈ {0, 1, 2,''' ) k + 1}. In this paper we prove that, if k ≥ 2 and G is a k-connected graph of order n such that Σ_i=1￣k si(Y) + 2sk+1(Y) n - 1 for each Y ∈ Ik+1(G),then G is hamiltonian. This theorem generalizes several well-known sufficient conditions for graphs to be hamiltonian.

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