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6 papers · 1 filter
Recent Progress in Graph Pebbling
Glenn Hurlbert
The subject of graph pebbling has seen dramatic growth recently, both in the number of publications and in the breadth of variations and applications. Here we update the reader on…
An application of graph pebbling to zero-sum sequences in abelian groups
Shawn Elldge, Glenn H. Hurlbert
A sequence of elements of a finite group G is called a zero-sum sequence if it sums to the identity of G. The study of zero-sum sequences has a long history with many important app…
The Cover Pebbling Number of Graphs
Betsy Crull, Tammy Cundiff, Paul Feltman +4
A pebbling move on a graph consists of taking two pebbles off of one vertex and placing one pebble on an adjacent vertex. In the traditional pebbling problem we try to reach a spec…
Girth, Pebbling, and Grid Thresholds
Andrzej Czygrinow, Glenn Hurlbert
In this note we answer a question of Hurlbert about pebbling in graphs of high girth. Specifically we show that for every g there is a Class 0 graph of girth at least g. The proof…
Pebbling in Dense Graphs
Andrzej Czygrinow, Glenn Hurlbert
A configuration of pebbles on the vertices of a graph is solvable if one can place a pebble on any given root vertex via a sequence of pebbling steps. The pebbling number of a grap…
Thresholds for families of multisets, with an application to graph pebbling
Airat Bekmetjev, Graham Brightwell, Andrzej Czygrinow +1
In this paper we prove two multiset analogs of classical results. We prove a multiset analog of Lovasz's version of the Kruskal-Katona Theorem and an analog of the Bollobas-Thomaso…