A Short Proof that the List Packing Number of any Graph is Well Defined

List packing is a notion that was introduced in 2021 (by Cambie et al.). The list packing number of a graph $G$, denoted ${\chi }_{\mathrm{\ell }}^{\ast }(G)$, is the least $k$ such that for any list assignment $L$ that assigns $k$ colors to each vertex of $G$, there is a set of $k$ proper $L$-colorings of $G$, $\{f_1,\dots ,f_k\}$, with the property $f_i(v)\mathrm{\ne }{f}_j(v)$ whenever $1\le i<j\le k$ and $v\in V(G)$. We present a short proof that for any graph $G$, ${\chi }_{\mathrm{\ell }}^{\ast }(G)\le \mathrm{\mid }V(G)\mathrm{\mid }$. Interestingly, our proof makes use of Galvin’s celebrated result that the list chromatic number of the line graph of any bipartite multigraph equals its chromatic number.