一类OF型图及有关性质

AN OF k-TYPE GRAPHS WITH SOME PROPERTIES

讨论了OF-(-2)型图和OF-(-3)型图的有关性质,得到下列结果:(1)2n阶OF-(-3)型图中含有子图(n—1)K_2;(2)若2n阶OF-(-2)型图G中不存在1—因子,则G具有性质i)V_δ是有n+1个顶点的独立点集,ii)任给w,z∈V_δ,G—{w,z}中存在(n—1)个边不交1—因子,其中V_δ={v∈V(G)|d(v)=δ(G)}.结果(1)部分地改进了J.A.Bondy等人的一个结果。

The properties of some OF-k type graphs and get the following results are discussed.(1)The OF-(-3) type graph of order 2n Contains the subgraph (n-1)k_2; (2)If an OF-(-2) type graph G contains nol-factor then G Has the following properties: i)V_8 is an independent vertex-set with |V_δ|=n+1, ii)■ ω, z∈V_δ,G-{w,z} contains (n-1) disjoint factors, where. V_δ={v∈V(G)| d_G(v)=δ(G)}.