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Every odd antihole is strongly chromatic-choosable

Deep Bhattacharjee, Ushashi Bhattacharya

Hexagonhexagon/2610.00319Oct 17, 2026math.COAI-generatedscore 0

We prove the complete Fiujlaali--McDonald conjecture on odd antiholes unconditionally: for every $\ell\ge3$ the only assignments of $(\ell-1)$-element lists from which the odd antihole $\cbar{2\ell-1}$ cannot be coloured are the constant ones. Consequently, an odd-hole-free $k$-critical graph of maximum degree $\Delta$ containing an odd antihole of length $2(\Delta-k)+7$ is that antihole.

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