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A separator theorem for chordal graphs. (English) Zbl 0551.05049
A graph is called chordal if every cycle of it of length at least four has a chord. In the paper it is proved: Let G be a chordal graph with n vertices and m edges. Then G has a set of O(\(\sqrt{m})\) vertices whose removal leaves no connected component with more than n/2 vertices. Moreover, an O(m) time algorithm for finding the separating set is presented.
Reviewer: P.Horak

MSC:
05C40 Connectivity
68R10 Graph theory (including graph drawing) in computer science
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[1] Properties of acyclic database schemesProc. 13th Annual ACM Symposium on Theory of Computing1981355362
[2] Dirac, G. A., On rigid circuit graphs, Abh. Math. Sem. Univ. Hamburg, 25, 71, (1961) · Zbl 0098.14703
[3] Djidjev, HristoNicolov, On the problem of partitioning planar graphs, SIAM J. Algebraic Discrete Methods, 3, 229, (1982) · Zbl 0503.05057
[4] Fulkerson, D. R.; Gross, O. A., Incidence matrices and interval graphs, Pacific J. Math., 15, 835, (1965) · Zbl 0132.21001
[5] Ph.D. ThesisGraph separator theorems and sparse Gaussian eliminationStanford UniversityStanford, CA1980
[6] Gilbert, JohnR.; Hutchinson, JoanP.; Tarjan, RobertEndre, A separator theorem for graphs of bounded genus, J. Algorithms, 5, 391, (1984) · Zbl 0556.05022
[7] Hajnal, András; Surányi, János, Über die auflösung von graphen in vollständige teilgraphen, Ann. Univ. Sci. Budapest. Eötvös. Sect. Math., 1, 113, (1958) · Zbl 0093.37801
[8] Jordan, Camille, Sur LES assemblages de lignes, Journal Reine Angew. Math., 70, 185, (1869) · JFM 02.0344.01
[9] A layout for the shuffle-exchange networkTechnical reportCMU-CS-80-139Carnegie-Mellon Univ. Department of Computer SciencePittsburgh, PA1980
[10] New lower bound techniques for VLSIProc. 22nd Annual IEEE Symposium on Foundations of Computer Science1981112
[11] Area-efficient graph layouts (for VLSI)Proc. 21st Annual IEEE Symposium on Foundations of Computer Science1980270281 · Zbl 1392.68055
[12] Memory bounds for the recognition of context-free and context-sensitive languagesIEEE Conference Record on Switching Theory and Logical Design1965191202
[13] Lipton, RichardJ.; Rose, DonaldJ.; Tarjan, RobertEndre, Generalized nested dissection, SIAM J. Numer. Anal., 16, 346, (1979) · Zbl 0435.65021
[14] Lipton, RichardJ.; Tarjan, RobertEndre, Applications of a planar separator theorem, SIAM J. Comput., 9, 615, (1980) · Zbl 0456.68077
[15] Lipton, RichardJ.; Tarjan, RobertEndre, A separator theorem for planar graphs, SIAM J. Appl. Math., 36, 177, (1979) · Zbl 0432.05022
[16] Rose, DonaldJ.; Read, R. C., A graph-theoretic study of the numerical solution of sparse positive definite systems of linear equations, Graph theory and computing, 183, (1972), Academic Press, New York · Zbl 0266.65028
[17] Rose, DonaldJ., On simple characterizations of k-trees, Discrete Math., 7, 317, (1974) · Zbl 0285.05128
[18] Rose, DonaldJ., Triangulated graphs and the elimination process, J. Math. Anal. Appl., 32, 597, (1970) · Zbl 0216.02602
[19] Rose, DonaldJ.; Tarjan, R. Endre; Lueker, GeorgeS., Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., 5, 266, (1976) · Zbl 0353.65019
[20] Yannakakis, Mihalis, Computing the minimum fill-in is NP-complete, SIAM J. Algebraic Discrete Methods, 2, 77, (1981) · Zbl 0496.68033
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