K_(1,4)自由模k的泛圈图的注记(英文)

A Note on Pancyclicity Mod k of K_(1,4)-Free Graph

给出关于K1,4自由模k的泛圈图的注记,证明了当条件弱化时已有结论的正确性,得到更一般意义下的模k的泛圈图,即每个2-连通的K1,4自由图G中,如果存在4个度都不小于k+1的点,其中一点u的邻域N(u)为3个不相交子集的并,其余3个点恰好分别属于以上3个子集,那么可得该图G是模k的泛圈图(k≥3).

In this paper,we gave out a note on pancyclicity mod k of Kl.4-free graph. It is proveded that the same conclusion is true under weakening the conditions in theroem and the more general pancyclicity mod k graph should be gotten,that is,in every 2-connected K1,4-free graph G, if there exist f6ur vertices whose degree is not smaller than k＋1 ,assume that one of the four vertices is u and N（u） （the neighborhood of u） is the union of three disjoint subsets,to which another three vertices just belong respectively,then it is still obtained.that G is pancyclic rood k,in which k≥3.