C.-Q. Zhang
The second circuit conjecture and cycle double cover conjecture

Abstract. The Cycle Double Cover Conjecture (CDC) was proposed independently by P.D. Seymour (1979) and G. Szekeres (1973). The conjecture is easy to state: For every 2-connected graph, there is a family of circuits such that every edge is contained in precisely two members of the family. This talk will survey some approaches to this well-known open problem in graph theory.

It was asked by Seymour that, for every cubic, bridgeless graph G and every circuit C of G, whether or not G contains a circuit C' distinct from C with V(C ) ⊆ V(C') (The Second Circuit Problem).

This problem, if true, implies the famous cycle double cover conjecture. Although a counterexample was discovered by Fleischner (1994), the Second Circuit Problem remains as a promising approach to a CDC conjecture.

In this talk, we will survey some old and recent results, and propose some modifications of this problem and possible approaches to CDC conjecture