汉米尔顿图泛圈性的奥尔型条件

THE ORE-TYPE CONDITIONS ON PANCYCLISM OF HAMILTONIAN GRAPHS

本文所说的图是简单图,未定义的术语见[1,2].n 阶图 G,n≥3,若有长为 n 的圈,则说 G 是汉米尔顿图;若对每个 k,3≤k≤n,G 含有长为 k 的圈,则说 G 是泛圈图.定理1.在 n 阶图 G 中,若对任何点对 x,y∈V(G),xy(?)E(G),都有 d(x)+d(y)≥n,则 G 是汉米尔顿图.

In this paper,it is proved that if G is a hamiltonian graph of order n,n≥50,and d(x)+d(y)>(4/5)n whenever xy(?)E(G),x,y ∈V(G),then G is pancyclic orbipartite;the bound (4/5)n is the best possible.