The Shortest Cycle Cover Conjecture

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For a bridgeless graph GG, let scc(G)scc(G) denote the length of a shortest cycle cover of GG. Shortest Cycle Cover Conjecture. If GG is a bridgeless graph, then

scc(G)≤75∣E(G)∣.scc(G)\leq \frac{7}{5}|E(G)|.

This conjecture gives a sharp proposed upper bound for shortest cycle covers and is related in the paper to the parameter T(G)T(G). It remains open.

References

Primary source

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

Additional references

2 papers in this index state this conjecture (2020–2025). The statement above is taken from the most recent of them; the others are arXiv:2004.14049.

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