摘要
Chvatal-Erdos定理指出如果G是阶数n≥3的图,且κ(G)≥α(G),那么G是Hamilton图;如果κ(G)>α(G),那么G是Hamilton连通图。我们在连通度足够大的情况下用限制更弱的最小度和独立数条件之间的关系取代原有的连通度和独立数条件之间的关系得到了一些新的结果。我们将证明如果G是阶数为n的图,n充分大,k是大于等于3的正整数,使得κ(G)≥2k~2+4k+1,δ(G)>(n+k~2-2k)/k,并且δ(G)>α(G)+k-2,那么G是Hamilton连通图。
The Chvatal-Erdos theorems imply that if G is a graph of order n≥3 withκ(G)≥α(G), then G is hamiltonian, and ifκ(G) >α(G),then G is hamiltonian-connected. We generalize these results by replacing the connectivity and independence number conditions with a weaker minimum degree and independence number conditions in the presence of sufficient connectivity.
We show that if G is a graph of order n and k≥3 is a positive integer such thatκ(G)≥2k~2+4k + 1 ,δ(G)>(n + k~2-2k)/k , andδ(G)>α(G) + k-2 ,then G is hamiltonian-connected.
引文
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