Discoveries / combinatorics

Kaul-Mudrock Conjecture on the Unlabeled List Color Function

Donner proved in 1992 that the list color function $P_\ell(G,k)$ equals the chromatic polynomial $P(G,k)$ once $k$ is large. Kaul and Mudrock asked whether the analogue holds for Hanlon's unlabeled chromatic polynomial, and could not settle even the edgeless graph, which they posed as a conjecture. The conjecture is true, and it implies that a disconnected graph satisfies the unlabeled analogue of Donner's result whenever all of its components do.