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Keywords:
bridgeless graph; components of an even factor; specified edge
bridgeless graph; components of an even factor; specified edge
Summary:
An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Let $G$ be a bridgeless simple graph with minimum degree at least $3$. Jackson and Yoshimoto (2007) showed that $G$ has an even factor containing two arbitrary prescribed edges. They also proved that $G$ has an even factor in which each component has order at least four. Moreover, Xiong, Lu and Han (2009) showed that for each pair of edges $e_1$ and $e_2$ of $G$, there is an even factor containing $e_1$ and $e_2$ in which each component containing neither $e_1$ nor $e_2$ has order at least four. In this paper we improve this result and prove that $G$ has an even factor containing $e_1$ and $e_2$ such that each component has order at least four.
References:
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