Geodesic
Edge-Connectivity and Edges of Even Factors of Graphs
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 357-364

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An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Jackson and Yoshimoto showed that if G is a 3-edge-connected graph with |G| ≥ 5 and v is a vertex with degree 3, then G has an even factor F containing two given edges incident with v in which each component has order at least 5. We prove that this theorem is satisfied for each pair of adjacent edges. Also, we show that each 3-edge-connected graph has an even factor F containing two given edges e and f such that every component containing neither e nor f has order at least 5. But we construct infinitely many 3-edge-connected graphs that do not have an even factor F containing two arbitrary prescribed edges in which each component has order at least 5.
Keywords: 3-edge-connected graph, 2-edge-connected graph, even factor, component 
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Haghparast, Nastaran; Kiani, Dariush. Edge-Connectivity and Edges of Even Factors of Graphs. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 2, pp. 357-364. http://geodesic.mathdoc.fr/item/DMGT_2019_39_2_a4/