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Graham's pebbling conjecture on products of cycles

✍ Scribed by David S. Herscovici

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 113 KB
Volume: 42
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10080

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✦ Synopsis

Abstract

Chung defined a pebbling move on a graph G to be the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The pebbling number of a connected graph is the smallest number f(G) such that any distribution of f(G) pebbles on G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. Graham conjectured that for any connected graphs G and H, f(G×H)≤ f(G)f(H). We prove Graham's conjecture when G is a cycle for a variety of graphs H, including all cycles. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 141–154, 2003

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