Even factors of graphs

Jian Cheng (), Cun-Quan Zhang () and Bao-Xuan Zhu ()
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Jian Cheng: West Virginia University
Cun-Quan Zhang: West Virginia University
Bao-Xuan Zhu: Jiangsu Normal University

Journal of Combinatorial Optimization, 2017, vol. 33, issue 4, No 10, 1343-1353

Abstract: Abstract An even factor of a graph is a spanning subgraph in which each vertex has a positive even degree. Favaron and Kouider (J Gr Theory 77:58–67, 2014) showed that if a simple graph G has an even factor, then it has an even factor F with $$|E(F)| \ge \frac{7}{16} (|E(G)| + 1)$$ | E ( F ) | ≥ 7 16 ( | E ( G ) | + 1 ) . This ratio was improved to $$\frac{4}{7}$$ 4 7 recently by Chen and Fan (J Comb Theory Ser B 119:237–244, 2016), which is the best possible. In this paper, we take the set of vertices of degree 2 (say $$V_{2}(G)$$ V 2 ( G ) ) into consideration and further strengthen this lower bound. Our main result is to show that for any simple graph G having an even factor, G has an even factor F with $$|E(F)| \ge \frac{4}{7} (|E(G)| + 1)+\frac{1}{7}|V_{2}(G)|$$ | E ( F ) | ≥ 4 7 ( | E ( G ) | + 1 ) + 1 7 | V 2 ( G ) | .

Keywords: Spanning subgraph; Maximum even factor; 2-Factor; Extremal graph theory (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0038-4

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