科研之友
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摘要
A graph G is supereulerian if G has a spanning eulerian subgraph. We use SL to denote the families of supereulerian graphs. In 1995, Zhi-Hong Chen and Hong-Jian Lai presented the following open problem [2, problem 8.8] : Determine
L = (minmax)(G is an element of SL - {K1}) {vertical bar E(H)vertical bar/vertical bar E(G)vertical bar : H is a spanning eulerian subgraph of G}
For a graph G, O(G) denotes the set of all odd-degree vertices of G. Let G be a simple graph and vertical bar O(G)vertical bar = 2k. In this note, we show that if G is an element of SL and k <= 2, then L >= 2/3.
- 出版日期2010-10
- 单位重庆工商大学
