Geodesic
The choice number versus the chromatic number for graphs embeddable on orientable surfaces
Brahadeesh Sankarnarayanan1 ; Niranjan Balachandran1
1Indian Institute of Technology Bombay
The electronic journal of combinatorics, Tome 28 (2021) no. 4
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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 $\Theta(\sqrt{g})$, and moreover for graphs with chromatic number of the order $o(\sqrt{g}/\log_{2}(g))$ the largest gap is of the order $o(\sqrt{g})$.
DOI : 10.37236/10263
Classification : 05C15, 05C10, 05C35, 05C75
Mots-clés : \(k\)-choosability, list chromatic number

Brahadeesh Sankarnarayanan  1   ; Niranjan Balachandran  1

1 Indian Institute of Technology Bombay 
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Brahadeesh Sankarnarayanan; Niranjan Balachandran. The choice number versus the chromatic number for graphs embeddable on orientable surfaces. The electronic journal of combinatorics, Tome 28 (2021) no. 4. doi: 10.37236/10263

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