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A Lower Bound for Partial List Colorings

Glenn G. Chappell
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Abstract

Let G be an n-vertex graph with list-chromatic number $χ_\ell$. Suppose each vertex of G is assigned a list of t colors. Albertson, Grossman, and Haas conjecture that at least $t n / {χ_\ell}$ vertices can be colored from these lists. We prove a lower bound for the number of colorable vertices. As a corollary, we show that at least 6/7 of the conjectured number can be colored.

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Glenn G. Chappell. 1998-05-13. A Lower Bound for Partial List Colorings. https://arxiv.org/abs/math/9805066

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