Generalizations of Graham鈥檚 pebbling conjecture

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• 作者：David S. Herscovici^a ; ^{David.Herscovici@quinnipiac.edu} ; Benjamin D. Hester^b ; ^{benjamin@mathpost.la.asu.edu} ; Glenn H. Hurlbert^b ; ^{hurlbert@asu.edu}
• 关键词：Pebbling ; Graham&rsquo ; s conjecture ; Generalizations
• 刊名：Discrete Mathematics
• 出版年：2012
• 期刊代码：47_0012365x
• 类别：cp
• 出版时间：6 August, 2012
• 卷：312
• 期：15
• 页码：2286-2293
• 文件大小：239 K

摘要

We investigate generalizations of pebbling numbers and of Graham鈥檚 pebbling conjecture that , where is the pebbling number of the graph . We develop new machinery to attack the conjecture, which is now twenty years old. We show that certain conjectures imply others that initially appear stronger. We also find counterexamples that shows that Sj枚strand鈥檚 theorem on cover pebbling does not apply if we allow the cost of transferring a pebble from one vertex to an adjacent vertex to depend on the weight of the edge and we describe an alternate pebbling number for which Graham鈥檚 conjecture is demonstrably false.