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arXiv · 2102.06993

The choice number versus the chromatic number for graphs embeddable on orientable surfaces

Niranjan Balachandran·Brahadeesh Sankarnarayanan
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Abstract

We show that for loopless $6$-regular triangulations on the torus the gap between the choice number and chromatic number is at most $2$. We also show that the largest gap for graphs embeddable in an orientable surface of genus $g$ is of the order $Θ(\sqrt{g})$, and moreover for graphs with chromatic number of the order $o(\sqrt{g}/\log_{2}(g))$ the largest gap is of the order $o(\sqrt{g})$.

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Niranjan Balachandran, Brahadeesh Sankarnarayanan. 2021-06-07. The choice number versus the chromatic number for graphs embeddable on orientable surfaces. https://doi.org/10.37236/10263

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