Packing list‐colorings

Abstract List coloring is an influential and classic topic in graph theory. We initiate the study of a natural strengthening this problem, where instead one list‐coloring, we seek many parallel. Our explorations have uncovered potentially rich seam interesting problems spanning chromatic Given ‐list‐assignment , which assignment list colors to each vertex existence pairwise‐disjoint proper colorings using from these lists. may refer as list‐packing . Using mix combinatorial probabilistic methods, set out some basic upper bounds on smallest for such always guaranteed, terms number vertices, degeneracy, maximum degree, or (list) (The reader might already find it that minimal well defined.) also pursue more focused case when bipartite graph. results do not yet rule tantalising prospect above too much larger than number. has taken inspiration strong number, explore generalizations problem same spirit.