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Even factor of bridgeless graphs containing two specified edges. (English) Zbl 07031701
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 $$3$$. B. Jackson and K. Yoshimoto [Discrete Math. 307, No. 22, 2775–2785 (2007; Zbl 1127.05080)] 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, L. Xiong et al. [Discrete Math. 309, No. 8, 2417–2423 (2009; Zbl 1214.05139)] 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.
##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
##### Citations:
Zbl 1127.05080; Zbl 1214.05139
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