The large even-subgraph 5-cycle double cover conjecture

A 5-cycle double cover (55-CDC) of a graph GG is a collection C=(E0,,E4){\cal C}=(E_0,\ldots,E_4) of five cycles such that every edge belongs to exactly two of them. Large even-subgraph 5-CDC conjecture. Every bridgeless graph GG admits a 55-CDC C=(E0,,E4){\cal C}=(E_0,\ldots,E_4) such that

E035E(G).|E_0|\geq \frac{3}{5}|E(G)|.

The paper presents this as a seemingly stronger version of the 5-cycle double cover conjecture and notes that the Petersen coloring conjecture implies its restriction to cubic graphs. The general statement remains open.

Sources & referencesView supporting material

Primary source

Giuseppe Mazzuoccolo and Vahan Mkrtchyan, “Expanding vertices to triangles in cubic graphs”, arXiv:2504.19201 (2025).

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