Odd-minor Duchet–Meyniel conjecture of Ji, Song, Weiss, and Zhang

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Let GG be a graph of order nn, let α(G)\alpha(G) denote its independence number, and let oh(G)oh(G) be the largest integer ℓ\ell such that GG has an odd KℓK_\ell minor.

Odd-minor Duchet–Meyniel conjecture. For any graph GG of order nn,

oh(G)≥⌈nα(G)⌉.oh(G)\geq \left\lceil\frac{n}{\alpha(G)}\right\rceil.

This is the odd-minor analogue of the Duchet–Meyniel conjecture and is stronger than the corresponding lower bound obtained by replacing oh(G)oh(G) with the ordinary minor parameter. The source does not state whether it has been resolved.

References

Primary source

Yuqing Ji, Yue Wang, Yujun Yang and Xia Zhang, “Odd clique minors and chromatic bounds of 3K_1, paraglider-free graphs”, arXiv:2509.00929 (2025).

Additional references

2 papers in this index state this conjecture (2025). The statement above is taken from the most recent of them; the others are arXiv:2505.07727.

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