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Clique Partitions of Chordal Graphs†

Published online by Cambridge University Press:  12 September 2008

Paul Erdős ,
Edward T. Ordman  and
Yechezkel Zalcstein
Paul Erdős
Affiliation:
Mathematical Institute, Hungarian Academy of Sciences
Edward T. Ordman
Affiliation:
Memphis State University, Memphis, TN 38152, U.S.A.
Yechezkel Zalcstein
Affiliation:
Division of Computer and Computation Research, National Science Foundation Washington, D.C. 20550, U.S.A.
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Abstract

To partition the edges of a chordal graph on n vertices into cliques may require as many as n2/6 cliques; there is an example requiring this many, which is also a threshold graph and a split graph. It is unknown whether this many cliques will always suffice. We are able to show that (1 − c)n2/4 cliques will suffice for some c > 0.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 4 , December 1993 , pp. 409 - 415
Copyright
Copyright © Cambridge University Press 1993

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