Euler生成子图边数的一个定理

A Theorem on the Number of Edges of Spanning Eulerian Subgraphs

证明了 :设G=(V ,E)是 2 -边连通的简单图 ,｜V｜ =n ,δ(G)是G的最小度 ,若δ(G) ≥max{4,n- 45 }时 ,G存在Euler生成子图H ,使得｜E(H) ｜ /｜E(G) ｜≥ 2 /3;即此时Catlin的 2 /3———猜想成立。

Let G=(V,E) be a 2_edge_connected simple graph on n vertices, δ(G) is the minimum of G. It has been proved that if δ(G) ≥max｛4, n-45 ｝,then G has a spanning eulerian subgraph H with ｜E(H)｜/｜E(G)｜ ≥2/3。