Thresholds for families of multisets, with an application to graph pebbling Original Research Article

In this paper we prove two multiset analogs of classical results. We prove a multiset analog of Lovászʹs version of the Kruskal–Katona Theorem and an analog of the Bollobás–Thomason threshold result. As a corollary we obtain the existence of pebbling thresholds for arbitrary graph sequences. In addition, we improve both the lower and upper bounds for the ‘random pebbling’ threshold of the sequence of paths.