# Choice numbers and coloring numbers - the infinite case

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Menachem Kojman, Ben Gurion University and IAS
Fine Hall 224

The choice number or list-chromatic number $\chi_\ell(G)$ of a graph $G=(V,E)$ is the minimum $k$ such that for every assignment of a list $s(v)$ of $k$ colors to each $v\in V$ there exists a proper coloring $c$ of $V$ that colors each $v$ by a color from $s(v)$. The coloring number $col(G)$ of $G$ is the minimum $k$ such that there is an enumeration $V=\{v_0,v_1,\dots,v_{n-1}\}$ satisfying that for each \$i