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Weight choosability of graphs

✍ Scribed by Tomasz Bartnicki; Jarosław Grytczuk; Stanisław Niwczyk

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 155 KB
Volume: 60
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20354

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✦ Synopsis

Abstract

Suppose the edges of a graph G are assigned 3‐element lists of real weights. Is it possible to choose a weight for each edge from its list so that the sums of weights around adjacent vertices were different? We prove that the answer is positive for several classes of graphs, including complete graphs, complete bipartite graphs, and trees (except K~2~). The argument is algebraic and uses permanents of matrices and Combinatorial Nullstellensatz. We also consider a directed version of the problem. We prove by an elementary argument that for digraphs the answer to the above question is positive even with lists of size two. © 2008 Wiley Periodicals, Inc. J Graph Theory 60: 242–256, 2009

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