# Cycle Double Covers via Kotzig Graphs

## TL;DR

This paper proves that certain 2-connected cubic graphs have a cycle double cover if they contain a specific spanning subgraph composed of even-vertex components, including cycles and Kotzig graph subdivisions.

## Contribution

It introduces new conditions involving Kotzig graphs that guarantee the existence of cycle double covers in 2-connected cubic graphs.

## Key findings

- Every 2-connected cubic graph with the specified spanning subgraph has a cycle double cover.
- The result extends previous knowledge by incorporating Kotzig graphs into the cycle double cover problem.
- The paper provides a new structural criterion for cycle double covers in cubic graphs.

## Abstract

We show that every $2$-connected cubic graph $G$ has a cycle double cover if $G$ has a spanning subgraph $F$ such that (i) every component of $F$ has an even number of vertices (ii) every component of $F$ is either a cycle or a subdivision of a Kotzig graph and (iii) the components of $F$ are connected to each other in a certain general manner.