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arXiv · 1311.1251

Painting Squares in $Δ^2-1$ Shades

Daniel W. Cranston·Landon Rabern
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Abstract

Cranston and Kim conjecture that if $G$ is a connected graph with maximum degree $Δ$ and $G$ is not a Moore Graph, then $χ_l(G^2) \le Δ^2-1$; here $χ_l$ is the list chromatic number. We prove their conjecture; in fact, this upper bound holds even for online list chromatic number.

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Daniel W. Cranston, Landon Rabern. 2014-01-30. Painting Squares in $Δ^2-1$ Shades. https://arxiv.org/abs/1311.1251

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