A Lower Bound for Partial List Colorings

Details A Lower Bound for Partial List Colorings A Lower Bound for Partial List Colorings

1998-05-13

arxiv.org/abs/math/9805066v1

Mathematics

Combinatorics

4 pages, no figures

Scientific paper

Let G be an n-vertex graph with list-chromatic number $\chi_\ell$. Suppose
each vertex of G is assigned a list of t colors. Albertson, Grossman, and Haas
conjecture that at least $t n / {\chi_\ell}$ 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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