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Discussiones Mathematicae Graph Theory 25(1-2) (2005) 167-182
DOI: https://doi.org/10.7151/dmgt.1270

ARITHMETICALLY MAXIMAL INDEPENDENT SETS IN INFINITE GRAPHS

Stanisław Bylka

Institute of Computer Science
Polish Academy of Sciences
21 Ordona street, 01-237 Warsaw, Poland
e-mail: bylka@ipipan.waw.pl

Abstract

Families of all sets of independent vertices in graphs are investigated. The problem how to characterize those infinite graphs which have arithmetically maximal independent sets is posed. A positive answer is given to the following classes of infinite graphs: bipartite graphs, line graphs and graphs having locally infinite clique-cover of vertices. Some counter examples are presented.

Keywords: infinite graph, independent set, arithmetical maximal set, line graph.

2000 Mathematics Subject Classification: 05C69, 05C65, 05D05.

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Received 28 November 2003
Revised 8 March 2005