Cycle Double Cover Conjecture

TL;DR

This paper claims to prove the cycle double cover conjecture, stating that every bridgeless graph has a cycle cover where each edge appears exactly twice, using induction on the number of edges.

Contribution

The paper provides a proof of the long-standing cycle double cover conjecture for bridgeless graphs using an inductive approach.

Findings

Proof of the cycle double cover conjecture for all bridgeless graphs

Inductive method to construct cycle covers including added edges

Validation of the conjecture through mathematical induction

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.