Strong Circuit Double Cover of Some Cubic Graphs. Issue 2 (14th April 2014) - Miao, Zhengke; Tang, Wenliang; Zhang, Cun‐Quan
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 <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qw7ntbz" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />H=G−C</alternatives> contains a Hamilton path or a Y‐tree of order less than 14, then G has a CDC containing C; (2) if <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qw7nt9d" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />H=G−C</alternatives> is connected and <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh2qw7nt8v" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" />|V(H)|≤6</alternatives>, then G has a CDC containing C.