The Short Cycle Cover Conjecture for bridgeless graphs

Let $G$ be a bridgeless graph with $m$ edges, and let the length of a cycle cover be the sum of the lengths of all cycles in the cover. Short Cycle Cover Conjecture. Every bridgeless graph with $m$ edges has a cycle cover of length at most $1.4m$.

This conjecture, attributed in the paper to Alon and Tarsi, concerns quantitative bounds on the shortest cycle cover. The paper proves upper bounds for bridgeless cubic graphs, but does not resolve the stated bound for all bridgeless graphs.