English

Cycle Double Cover Conjecture

Combinatorics 2014-04-08 v3

Abstract

In this paper, a proof of the cycle double cover conjecture is presented. The cycle double cover conjecture purports that if a graph is bridgeless, then there exists a list of cycles in the graph such that every edge in the graph appears in the list exactly twice. By applying induction on the number of edges in a bridgeless graph, I show that when an edge is added to a bridgeless graph, we can reform the cycle double cover to include that edge. By mathematical induction, this concludes the general CDC.

Keywords

Cite

@article{arxiv.1401.0908,
  title  = {Cycle Double Cover Conjecture},
  author = {P. Clarke},
  journal= {arXiv preprint arXiv:1401.0908},
  year   = {2014}
}

Comments

This paper has been withdrawn due to a critical error in the proof of theorem 3. Thanks to Prof. P. Seymour for highlighting the mistake

R2 v1 2026-06-22T02:39:19.607Z