二部图的E-H-不可收缩性

E-H-Unretractivity of Bipartite Graphs

中文关键词:  自同态么半群  不可收缩性  二部图.

英文关键词:endomorphism monoid  E-H-unretractivity  bipartite graph.

中文摘要:

      一个图$G$的自同态集合及半强自同态集合分别由$End(G)$及$hEnd(G)$表示.图$G$称为是E-H不可收缩的若$End(G)=hEnd(G)$.给出具有E-H不可收缩性的图的一般性特征似乎是个较困难的问题.二部图是一类重要的图族.本文 明确刻画了具有E-H不可收缩性的二部图的特征.

英文摘要:

      By $\End(G)$ and $h\End(G)$ we denote the set of endomorphisms and half-strong endomorphisms of a graph $G$ respectively. A graph $G$ is said to be E-H-unretractive if $\End(G)=h\End(G)$. A general characterization of an E-H-unretractive graph seems to be difficult. In this paper, bipartite graphs with E-H-unretractivity are characterized explicitly.