超欧拉路可合并有向图及半完全有向图（英文）

Supereulerian Path-mergeable and Semicomplete Digraphs

令D是一个严格有向图(无环与重弧),如果D含有一个生成欧拉子有向图,则称D是超欧拉的。文章主要研究路可合并有向图与半完全有向图成为超欧拉的充要条件,利用最大闭迹去寻找矛盾的方法证明了如果一个有向图D是一个路可合并有向图或半完全有向图,则D是超欧拉有向图当且仅当D是强连通的。

A digraph D is supereulerian if D has a spanning eulerian subdigraph. In this paper, we give sufficient and necessary conditions involving path-mergeable digraphs and semicomplete digraphs to be supereulerian. The method of finding the contradiction by using the maximum closed ditrail is proved that if D is a path-mergeable digraph or a semicomplete digraph, then D is supereulerian if and only if D is strong.