منابع مشابه
Girth, Pebbling, and Grid Thresholds
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 uses the so-called Erdős construction and employs a recent result proved by Czygrinow, Hurlbert, Kierstead and Trotter. We also use the Czygrinow et al. result to prove that Graham’s pebbling product conjecture holds ...
متن کاملCover Pebbling Thresholds for the Complete Graph
We obtain first-order cover pebbling thresholds of the complete graph for Maxwell Boltzmann and Bose Einstein configurations.
متن کاملThe Complexity of Pebbling and Cover Pebbling
This paper discusses the complexity of graph pebbling, dealing with both traditional pebbling and the recently introduced game of cover pebbling. Determining whether a configuration is solvable according to either the traditional definition or the cover pebbling definition is shown to be NP -complete. The problem of determining the cover pebbling number for an arbitrary demand configuration is ...
متن کاملPebbling and optimal pebbling in graphs
Given a distribution of pebbles on the vertices of a graph G, a pebbling move takes two pebbles from one vertex and puts one on a neighboring vertex. The pebbling number Π(G) is the least k such that for every distribution of k pebbles and every vertex r, a pebble can be moved to r. The optimal pebbling number ΠOPT (G) is the least k such that some distribution of k pebbles permits reaching eac...
متن کاملThresholds for families of multisets, with an application to graph pebbling
In this paper we prove two multiset analogs of classical results. We prove a multiset analog of Lovász’s 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 seque...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2006
ISSN: 0895-4801,1095-7146
DOI: 10.1137/s0895480102416374