Open Problem Garden - Cycle double cover conjecture - Comments

Claimed solution in the affirmative (re: Cycle double cover conjecture)

Andrew King — Tue, 07 Feb 2012 06:33:11 +0100

Alexander Souza has offered for review on arXiv a constructive solution in the affirmative.

http://arxiv.org/abs/1202.0569

Edit: Unless we are mistaken, the Petersen graph is a counterexample to Theorem 2. Furthermore there is an unresolved problem with Lemma 9.

Andrew King — Mon, 06 Feb 2012 07:59:38 +0100

No; consider the example of a graph which is itself a cycle. This has a unique cycle double cover, and the cycles are not distinct.

khaniki — Thu, 06 Oct 2011 14:36:14 +0200

should the cycles be distinct??

mdevos — Wed, 07 Mar 2007 12:27:48 +0100

Author(s): Seymour; Szekeres

Subject: Graph Theory » Basic G.T. » Cycles

Conjecture For every graph with no bridge, there is a list of cycles so that every edge is contained in exactly two.