A Lower Bound for Partial List Colorings
Glenn G. Chappell
Abstract
Let G be an n-vertex graph with list-chromatic number χ. Suppose each vertex of G is assigned a list of t colors. Albertson, Grossman, and Haas conjecture that at least t n / χ 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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