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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.)
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