笛卡尔积有向图的欧拉覆盖数

The Eulerian Cover Number of Cartesian Product Digraphs

如果有向图D包含一个生成欧拉子图,那么有向图D是超欧拉有向图;如果有向图D包含一个生成有向迹,那么有向图D是生成迹有向图。文章定义了有向图D的欧拉覆盖数并用符号ec(D)表示。此外,文章将证明ec(D_1)=1的强连通有向图D_1与ec(D_2)=2的有向图D2做笛卡尔积后的欧拉覆盖数。

A digraph D is supereulerian if D contains a spanning eulerian subdigraph,and is trailable if D contains a spanning ditrail.Let ec(D)denote the eulerian cover number of D.In this paper,we define the eulerian cover number of D.Moreover,the paper will prove the eulerian cover number of the cartesian product of strong digraph D1 with ec(D1)=1and the digraph D2 with ec(D2)=2.