On The Cycle Double Cover Problem

Details On The Cycle Double Cover Problem On The Cycle Double Cover Problem

2012-01-25

arxiv.org/abs/1201.5203v3

Mathematics

Combinatorics

23 pages, Two proofs of the cycle double cover (conjecture)! A proof of Goddyn's conjecture

Scientific paper

In this paper, for each graph G, a free edge set F is defined. To study the existence of cycle double cover, the naive cycle double cover of G and F have been defined and studied. In the main theorem, the paper, based on the Kuratowski minor properties, presents a condition to guarantee the existence of a naive cycle double cover for couple (G,F). As a result, the cycle double cover conjecture has been concluded. Moreover, Goddyn's conjecture - asserting if C is a cycle in bridgeless graph G, there is a cycle double cover of G containing C - will have been proved.

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