Odd-defect list edge-colouring bound

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Let GG be a graph, let dd be an odd integer, and let chd′(G)ch'_d(G) denote its dd-defective list chromatic index.

Odd-defect list edge-colouring conjecture. For every odd integer dd and for every graph GG,

chd′(G)≤⌈3Δ−13d−1⌉.ch'_d(G) \leq \left\lceil \frac{3\Delta - 1}{3d-1} \right\rceil.

This is a proposed extension of the defective edge-colouring bound to list edge colouring; the source notes that the corresponding announced result has a flaw outside a divisibility condition, so the conjecture remains open.

References

Primary source

Pierre Aboulker, Guillaume Aubian and Chien-Chung Huang, “Vizing's and Shannon's Theorems for defective edge colouring”, arXiv:2201.11548 (2022).

Additional references

3 papers in this index state this conjecture (2006–2022). The statement above is taken from the most recent of them; the others are arXiv:2109.06110, arXiv:math/0605234.

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