Induced matchings in intersection graphs

Discrete Mathematics

Volumn 278, Issue 1-3, 2004, Pages 1-9

  Cameron, Kathie ^a  

^a WILFRID LAURIER UNIVERSITY   (Canada)

Author keywords

Asteroidal triple free graph; Cocomparability graph; Induced matching; Interval filament graph; Polygon circle graph; Strong chromatic index

Indexed keywords

ALGORITHMS; MATHEMATICAL MODELS; PARALLEL PROCESSING SYSTEMS; POLYNOMIALS; PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

ASTEROIDAL TRIPLE-FREE GRAPH; COCOMPARABILITY GRAPH; INDUCED MATCHING; INTERVAL-FILAMENT GRAPH; POLYGON-CIRCLE GRAPH; STRONG CHROMATIC INDEX;

GRAPH THEORY;

EID: 1142263894     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disc.2003.05.001     Document Type: Article

References (30)

1. Bertossi A.A., Moretti S. Parallel algorithms on circular-arc graphs. Inform. Process. Lett. 33:1990;275-281.
2. Bouchet A. Circle graph obstructions. J. Combin. Theory Ser. B. 60:1994;107-144.
3. Broersma H.J., Kloks T., Kratsch D., Müller H. Independent sets in asteroidal triple-free graphs. SIAM J. Discrete Math. 12:1999;276-287.
4. Cameron K. Induced matchings. Discrete Appl. Math. 24:1989;97-102.
5. Cameron K. An algorithmic note on the Gallai-Milgram Theorem. Networks. 20:1990;43-48.
6. Ford L.R., Fulkerson D.R. Flows in Networks. 1962;Princeton University Press, Princeton, NJ.
7. Gallai T. Transitiv orientierb are graphen (German). Acta Math. Acad. Sci. Hungaricae. 18:1967;25-66.
8. Garey M.R., Johnson D.S., Miller G.L., Papadimitiou C.H. The complexity of coloring circular arcs and chords. SIAM J. Algebraic Discrete Methods. 1:1980;216-227.
9. Gavril F. Algorithms for minimum coloring, maximum clique, minimum covering by cliques, and maximum independent set of a chordal graph. SIAM J. Comput. 1:1972;180-187.
10. Gavril F. Algorithms on circular-arc graphs. Networks. 4:1974;357-369.
11. Gavril F. Maximum weight independent sets and cliques in intersection graphs of filaments. Inform. Process. Lett. 73:2000;181-188.
12. Gilmore P.C., Hoffman A.J. A characterization of comparability graphs and interval graphs. Canad. J. Math. 16:1964;539-548.
13. Golumbic M.C. Algorithmic Graph Theory and Perfect Graphs. 1980;Academic Press, New York.
14. Golumbic M.C., Hammer P.L. Stability in circular arc graphs. J. Algorithms. 9:1988;314-320.
15. Golumbic M.C., Laskar R.C. Irredundancy in circular-arc graphs. Discrete Appl. Math. 44:1993;79-89.
16. Golumbic M.C., Lewenstein M. New results on induced matchings. Discrete Appl. Math. 101:2000;157-165.
17. Golumbic M.C., Rotem D., Urrutia J. Comparability graphs and intersection graphs. Discrete Math. 43:1983;37-46.
18. Janson S., Kratochvíl J. Threshold functions for classes of intersection graphs. Discrete Math. 108:1992;307-326.
19. Chang Jou-Ming Induced matchings in asteroidal triple-free graphs. Discrete Appl. Math. 132:2003;67-78.
20. Ko C.W., Shepherd F.B. Bipartite domination and simultaneous matroid covers. SIAM J. Discrete Math. 16:2003;517-523.
21. E.G. Köhler, Graphs without asteroidal triples, Ph.D. Thesis, Technical University of Berlin, Cuvillier Verlag, Göttingen, 1999.
22. Kostochka A., Kratochvíl J. Covering and coloring polygon-circle graphs. Discrete Math. 163:1997;299-305.
23. Lekkerkerker C.G., Boland J.Ch. Representation of a finite graph by a set of intervals on the line. Fund. Math. 51:1962;45-64.
24. Minty G.J. On maximal independent sets of vertices in claw-free graphs. J. Combin. Theory Ser. B. 28:1980;284-304.
25. Naor J., Naor M., Schäeffer A.A. Fast parallel algorithms for chordal graphs. SIAM J. Comput. 18:1989;327-349.
26. Raychaudhuri A. On powers of interval and unit interval graphs. Congr. Numer. 59:1987;235-242.
27. Chongkye Rhee, Y. Daniel Liang, An NC algorithm for the clique cover problem and its application, Inform. Process. Lett. 57 (1996) 287-290.
28. Sbihi N. Algorithme de recherche d'un stable de cardinalité maximum dans un graphe sans étoile. Discrete Math. 29:1980;53-76. (in French).
29. Srinivasa Rao A., Pandu Rangan C. Optimal parallel algorithms on circular-arc graphs. Inform. Process. Lett. 33:1989;147-156.
30. Stockmeyer L.J., Vazirani V.V. NP-completeness of some generalizations of the maximum matching problem. Inform. Process. Lett. 15:1982;14-19.