Choosability of a weighted path and free-choosability of a cycle

Yves Aubry, Jean-Christophe Godin, Olivier Togni

A graph $G$ with a list of colors $L(v)$ and weight $w(v)$ for each vertex $v$ is $(L,w)$-colorable if one can choose a subset of $w(v)$ colors from $L(v)$ for each vertex $v$, suc…