# Short cycle covers of cubic graphs and intersecting 5-circuits

## TL;DR

This paper proves new upper bounds on the length of cycle covers in bridgeless cubic graphs, showing they can be covered efficiently with cycles, especially in cyclically 4-edge-connected cases.

## Contribution

It establishes improved bounds on cycle cover lengths for bridgeless cubic graphs, including special cases with cyclic connectivity, advancing understanding of cycle covers.

## Key findings

- Cycle cover length at most 212/135 times the number of edges for all bridgeless cubic graphs.
- Cycle cover length at most 47/30 times the number of edges for cyclically 4-edge-connected graphs.
- Provides explicit bounds improving previous results in the literature.

## Abstract

A cycle cover of a graph is a collection of cycles such that each edge of the graph is contained in at least one of the cycles. The length of a cycle cover is the sum of all cycle lengths in the cover. We prove that every bridgeless cubic graph with $m$ edges has a cycle cover of length at most $212/135 \cdot m \ (\approx 1.570 m)$. Moreover, if the graph is cyclically $4$-edge-connected we obtain a cover of length at most $47/30 \cdot m \approx 1.567 m$.