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On the chordality of a graph
Author(s) -
McKee Terry A.,
Scheinerman Edward R.
Publication year - 1993
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190170210
Subject(s) - combinatorics , mathematics , outerplanar graph , block graph , chordal graph , bounding overwatch , treewidth , discrete mathematics , graph , pathwidth , planar graph , line graph , computer science , artificial intelligence
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.