# Grossman, Sara

## Partial List Coloring ★★★

Author(s): Albertson; Grossman; Haas

\begin{conjecture} Let $G$ be a simple graph with $n$ vertices and list chromatic number $\chi_\ell(G)$. Suppose that $0\leq t\leq \chi_\ell$ and each vertex of $G$ is assigned a list of $t$ colors. Then at least $\frac{tn}{\chi_\ell(G)}$ vertices of $G$ can be colored from these lists. \end{conjecture}

Keywords: list assignment; list coloring