摘要
G表示一个图 ,若G有一个欧拉生成子图 ,则称G是超欧拉图。Catlin的 2 3—猜想 :设G是超欧拉图 ,G ≠K1,则G存在一个欧拉生成子图H ,使得｜E(H) ｜ ｜E(G) ｜≥ 2 3。笔者证明了对于Cayley图 ,猜想成立。
G is a graph,if G has a spanning Eulerian subgraph. G is a supereulerian graph. A conjecture on the Catlin's 2/3: suppose G is a supereulerian graph, and G≠K 1,then G has a spanning Eulerian subgraph H , and it renders ｜E(H)｜/｜E(G)｜≥2/3 . It is proved the conjecture is tenable to Cayley graph.
基金
国家自然科学基金! (NO .198710 6 6 )
重庆市教委资助项目
