A Note on the 3-Edge-Connected Supereulerian Graphs
暂无分享,去创建一个
For two integers l > 0 and k � 0, define C(l, k) to be the family of 2-edge connected graphs such that a graph G 2 C(l, k) if and only if for every bond SE(G) with |S| � 3, each component of G S has order at least (|V (G)| k)/l. In this note we prove that if a 3- edge-connected simple graph G is in C(10,3), then G is supereulerian if and only if G cannot be contracted to the Petersen graph. Our result extends an earlier result in (Supereulerian graphs and Petersen graph. JCMCC 1991, 9: 79-89) by Chen.
[1] Hong-Jian Lai,et al. Graphs without spanning closed trails , 1996, Discret. Math..
[2] Paul A. Catlin,et al. A reduction method to find spanning Eulerian subgraphs , 1988, J. Graph Theory.
[3] J. A. Bondy,et al. Graph Theory with Applications , 1978 .