Short Cycle Covers of Cubic Graphs and Intersecting 5-Circuits

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·m (≈ 1.570m). Moreover, if the graph is cyclically 4-edge-connected we obtain a cover of length at most 47/30·m ≈ 1.567m.