Strong Circuit Double Cover of Some Cubic Graphs
Zhengke Miao, Wenliang Tang, Cun‐Quan Zhang · Journal of Graph Theory · 2014
Let C be a given circuit of a bridgeless cubic graph G. It was conjectured by Seymour that G has a circuit double cover (CDC) containing the given circuit C. This conjecture (strong CDC [SCDC] conjecture) has been verified by Fleischner and Häggkvist for various families of graphs and circuits. In this article, some of these earlier results have been improved: (1) if contains a Hamilton path or a Y-tree of order less than 14, then G has a CDC containing C; (2) if is connected and , then G has a CDC containing C.