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On the chordality of a graph

✍ Scribed by Terry A. McKee; Edward R. Scheinerman

Publisher: John Wiley and Sons
Year: 1993
Tongue: English
Weight: 574 KB
Volume: 17
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190170210

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✦ Synopsis

Abstract

The chordality of a graph G = (V, E) is defined as the minimum k such that we can write E = E~1~ ∩ … ∩ E~k~ with each (V, E~i~) a chordal graph. We present several results bounding the value of this generalization of boxicity. Our principal result is that the chordality of a graph is at most its tree width. In particular, series‐parallel graphs have chordality at most 2. Potential strengthenings of this statement fail in that there are planar graphs with chordality 3 and series‐parallel graphs with boxicity 3. © 1993 John Wiley & Sons, Inc.

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