A Note on Graph Pebbling

dc.creatorCzygrinow, Andrzej
dc.creatorHurlbert, Glenn
dc.creatorKierstead, Hal
dc.creatorTrotter, Tom
dc.date2004-06-03
dc.date.accessioned2026-07-07T05:08:50Z
dc.date.available2026-07-07T05:08:50Z
dc.descriptionWe say that a graph G is Class 0 if its pebbling number is exactly equal to its number of vertices. For a positive integer d, let k(d) denote the least positive integer so that every graph G with diameter at most d and connectivity at least k(d) is Class 0. The existence of the function k was conjectured by Clarke, Hochberg and Hurlbert, who showed that if the function k exists, then it must satisfy k(d)=Ω(2^d/d). In this note, we show that k exists and satisfies k(d)=O(2^{2d}). We also apply this result to improve the upper bound on the random graph threshold of the Class 0 property.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/math/0406053
dc.identifierhttp://arxiv.org/abs/math/0406053
dc.identifierGraphs and Combinatorics 18 (2002), 219--225
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71419
dc.subjectCombinatorics
dc.subject05C35
dc.titleA Note on Graph Pebbling
dc.typetext

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