Even Cycles and Even 2-Factors in the Line Graph of a Simple Graph

[摘要] Let $G$ be a connected graph with an even number of edges. We show that if the subgraph of $G$ induced by the vertices of odd degree has a perfect matching, then the line graph of $G$ has a $2$-factor whose connected components are cycles of even length (

[学科分类] 离散数学和组合数学

[关键词] Cycle decomposition;2-factor;Oriented graphs;Line graph