Even factors of graphs |
| |
Authors: | Jian Cheng " target="_blank">Cun-Quan Zhang Bao-Xuan Zhu |
| |
Institution: | 1.Department of Mathematics,West Virginia University,Morgantown,USA;2.School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou,PR China |
| |
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 \(|E(F)| \ge \frac{7}{16} (|E(G)| + 1)\). This ratio was improved to \(\frac{4}{7}\) 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 \(V_{2}(G)\)) 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 \(|E(F)| \ge \frac{4}{7} (|E(G)| + 1)+\frac{1}{7}|V_{2}(G)|\). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|