Fractional List Packing for Layered Graphs

ABSTRACT The fractional list packing number of a graph is a graph invariant that has recently arisen from the study of disjoint list‐colourings. It measures how large the lists of a list‐assignment need to be to ensure the existence of a “perfectly balanced” probability distribution on proper ‐colourings, that is, such that at every vertex , every colour appears with equal probability . In this work we give various bounds on , which admit strengthenings for correspondence and local‐degree versions. As a corollary, we improve theorems on the related notion of flexible list colouring. In particular we study Cartesian products and ‐degenerate graphs, and we prove that is bounded from above by the pathwidth of plus one. The correspondence analogue of the latter is false for treewidth instead of pathwidth.