| The Chvatal-Erdos theorems imply that if G is a graph of order n≥3 withκ(g)≥α(g) ,then G ia Hamiltonion,and ifκ(g)>α(g) ,then G is Hamilton-connected. Jacobson and his team has got these results as below by using a variation of the connectivity and independence number conditions of the Chvatal-Erdos theorems with a weaker minimum degree and independence number condition:(i)Let G be a graph of sufficiently large order n and k≥3 a positive integer such thatκ(G)≥4k~2 +1,δ(G)>(n+k~2 -2k)/k.Ifδ(G)≥α(G)+k-2,then G is the graphHamilton-connected;(ii)Let G be a graph of sufficiently large order n and k = 3 or 4 such thatκ(G)≥k,δ(G)>(n+k~2-2k)/k,Ifδ(G)≥α(G)+k-2 then G is Hamilton-connected.In this paper,we will show that: Let G be a graph of sufficiently large order n and k = 5 such thatκ(G)≥k ,δ(G)>(n+k~2 -2k)/k ,Ifδ(G)≥α(G)+k-2 then G is Hamilton-connected... |
