Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-19T05:36:13.634Z Has data issue: false hasContentIssue false
  • English
  • Français

Maximal-clique partitions of interval graphs

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

Ma Shaohan  and
W. D. Wallis
Ma Shaohan
Affiliation:
Department of Computer Science, Shandong UniversityJinan People's Republic of China
W. D. Wallis
Affiliation:
Department of MathematicsSouthern Illinois UniversityCarbondale, Illinois 62901, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that if an interval graph possesses a maximal-clique partition then its clique covering and clique partition numbers are equal, and equal to the maximal-clique partition number. Moreover an interval graph has such a partition if and only if all its maximal cliques are edge-disjoint.

MSC classification

Secondary: 05C35: Extremal problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 2 , October 1988 , pp. 227 - 232
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Booth, K. S. and Leuker, G. S., ‘Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms’, J. Comput. System Sci. 13 (1976), 335–379.CrossRefGoogle Scholar
[2]Fulkerson, D. R. and Gross, O. A., ‘Incidence matrices and interval graphs’, Pacific J. Math. 15 (1965), 835–855.CrossRefGoogle Scholar
[3]Lekkerkerker, C. G. and Boland, J. Ch., ‘Representation of a finite graph by a set of intervals on the real line’, Fund. Math. 51 (1962), 54–64.Google Scholar
[4]Shaohan, Ma and Wallis, W. D., ‘Clique partitions of triangulated graphs’, Congress. Numer., to appear.Google Scholar
[5]Pullman, N. J., ‘Clique coverings of graphs IV: algorithms’, SIAM J. Comput. 13 (1984), 57–75.CrossRefGoogle Scholar
[6]Pullman, N. J., Shank, H. and Wallis, W. D., ‘Clique coverings of graphs V: maximal-clique partitions’, Bull. Austral. Math. Soc. 25 (1982), 337–356.CrossRefGoogle Scholar