Strong Circuit Double Cover of Some Cubic Graphs. Issue 2 (14th April 2014) - Miao, Zhengke
Abstract 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 H=G−C contains a Hamilton path or a Y‐tree of order less than 14, then G has a CDC containing C; (2) if H=G−C is connected and |V(H)|≤6, then G has a CDC containing C.