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Even factors of graphs

Author

Listed:
  • Jian Cheng

    (West Virginia University)

  • Cun-Quan Zhang

    (West Virginia University)

  • Bao-Xuan Zhu

    (Jiangsu Normal University)

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 ) | .

Suggested Citation

  • Jian Cheng & Cun-Quan Zhang & Bao-Xuan Zhu, 2017. "Even factors of graphs," Journal of Combinatorial Optimization, Springer, vol. 33(4), pages 1343-1353, May.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:4:d:10.1007_s10878-016-0038-4
    DOI: 10.1007/s10878-016-0038-4
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