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Almost all chordal graphs split

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

E. A. Bender ,
L. B. Richmond  and
N. C. Wormald
E. A. Bender
Affiliation:
Department of Mathematics University of California at San DiegoLa Jolla, California 92093, USA
L. B. Richmond
Affiliation:
Department of Combinatorics and Optimization University of WaterlooWaterloo, Ontario N2L 3G1, Canada
N. C. Wormald
Affiliation:
Department of Mathematics, Statistics and Computer Science University of NewcastleNew South Wales 2308, Australia
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Abstract

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A chordal graph is a graph in which every cycle of length at least 4 has a chord. If G is a random n-vertex labelled chordal graph, the size of the larget clique in about n/2 and deletion of this clique almost surely leaves only isolated vertices. This gives the asymptotic number of chordal graphs and information about a variety of things such as the size of the largest clique and connectivity.

MSC classification

Secondary: 05C99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 2 , April 1985 , pp. 214 - 221
Copyright
Copyright © Australian Mathematical Society 1985

References

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