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Graphs with unique maximal clumpings

✍ Scribed by Andreas Blass

Publisher: John Wiley and Sons
Year: 1978
Tongue: English
Weight: 322 KB
Volume: 2
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190020104

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✦ Synopsis

Abstract

A partition of the vertices of a graph is called a clumping if, for vertices in distinct partition classes, adjacency depends only on the partition classes, not on the specific vertices. We give a simple necessary and sufficient condition for a finite graph to have a unique maximal clumping. We also investigate the extent to which this and related results generalize to infinite graphs.

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