A Constructive Proof of the Cycle Double Cover Conjecture

TL;DR

This paper proves the cycle double cover conjecture for bridge-free graphs and provides a polynomial-time algorithm to construct such covers, confirming a long-standing open problem in graph theory.

Contribution

It offers a constructive proof of the cycle double cover conjecture and introduces an efficient algorithm for constructing cycle double covers.

Findings

Confirmed the cycle double cover conjecture for all bridge-free graphs.

Developed a polynomial-time algorithm for constructing cycle double covers.

Provided a constructive method that can be implemented algorithmically.

Abstract

The cycle double cover conjecture states that a graph is bridge-free if and only if there is a family of edge-simple cycles such that each edge is contained in exactly two of them. It was formulated independently by Szekeres (1973) and Seymour (1979). In this paper, we settle the conjecture in the affirmative. In particular, we give an algorithm, which inductively constructs a cycle double cover in polynomial time.