Maximum even factors of graphs

A spanning subgraph F of a graph G is called an even factor of G if each vertex of F has even degree at least 2 in F. Kouider and Favaron proved that if a graph G has an even factor, then it has an even factor F with |E(F)|≥916(|E(G)|+1). In this paper we improve the coefficient 916 to 47, which is...

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Bibliographic Details
Published in:Journal of combinatorial theory. Series B 2016-07, Vol.119, p.237-244
Main Authors: Chen, Fuyuan, Fan, Genghua
Format: Article
Language:English
Subjects:
2-Factor
Even graph
Large even factor
Spanning subgraph
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Summary:A spanning subgraph F of a graph G is called an even factor of G if each vertex of F has even degree at least 2 in F. Kouider and Favaron proved that if a graph G has an even factor, then it has an even factor F with |E(F)|≥916(|E(G)|+1). In this paper we improve the coefficient 916 to 47, which is best possible. Furthermore, we characterize all the extremal graphs, showing that if |E(H)|≤47(|E(G)|+1) for every even factor H of G, then G belongs to a specified class of graphs.
ISSN:0095-8956
1096-0902
DOI:10.1016/j.jctb.2016.03.002