Circuit double covers in special types of cubic graphs

6-cycle Double Covers of Cubic Graphs

A cycle double cover (CDC) of an undirected graph is a collection of the graph’s cycles such that every edge of the graph belongs to exactly two cycles. We describe a constructive method for generating all the cubic graphs that have a 6-CDC (a CDC in which every cycle has length 6). As an application of the method, we prove that all such graphs have a Hamiltonian cycle. A sense of direction is ...

Double covers of cubic graphs with oddness 4

We prove that a cubic 2-connected graph which has a 2-factor containing exactly 4 odd cycles has a cycle double cover. © 2004 Elsevier Inc. All rights reserved. MSC: 05C38; 05C40; 05C70

Strong Circuit Double Cover of Some Cubic Graphs

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: Contract grant sponsor: NSF-China;...

Circuit Covers in Series-Parallel Mixed Graphs

On semiextensions and circuit double covers

We introduce a concept of a semiextension of a cycle, and we conjecture a simple necessary and sufficient condition for its existence. It is shown that our conjecture implies a strong form of the circuit double cover conjecture. We prove that the conjecture is equivalent to its restriction to cubic graphs, and we show that it holds for every cycle which is a spanning subgraph of the given graph...