Zusammenfassung
Bäume sind im Zusammenhang mit Graphenalgorithmen und Anwendungen von Graphen von herausragender Bedeutung. In diesem Kapitel werden wichtige Verallgemeinerungen von Bäumen betrachtet, die weitgehende algorithmische Anwendungen erlauben. Ein zentraler Punkt ist dabei die Baumstruktur der maximalen Cliquen der im folgenden definierten chordalen Graphen.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Literaturhinweise
G.A. Dirac, On rigid circuit graphs, Abh. Math. Sem. Univ. Hamburg, 25 (1961), 71–76
P. Buneman, A characterization of rigid circuit graphs, Discr. Math., 9 (1974), 205–212
F. Gavril, The Intersection Graphs of Subtrees in Trees are exactly the Chordal Graphs, J. Combin. Theory Series B 16, 47–56, 1974
J.R. Walter, Representations of Chordal Graphs as Subtrees of a Tree, Journal of Graph Theory 2, 265–267, 1978
C. Berge, Hypergraphs, North Holland, 1989
C. Beeri, R. Fagin, D. Maier, and M. Yannakakis, On the desirability of acyclic database schemes, Journal of the Assoc. for Comput. Mach., 30, 3 (1983), 479–513
N. Goodman and O. Shmueli, Syntactic characterization of tree database schemes, Journal of the Assoc. for Comput. Mach. 30 (1983), 767–786
R. Fagin, Degrees of acyclicity for hypergraphs and relational database schemes, Journal of the Assoc. for Comput. Mach., 30 (1983), 514–550
M.C. Golumbic, Algorithmic aspects of intersection graphs and representation hypergraphs, Graphs and Combinatorics, 4 (1988), 307–321
P. Duchet, Classical perfect graphs: an introduction with emphasis on triangulated and interval graphs, Annals of Discr. Math., North Holland, 21 (1984), 67–96
C. Flament, Hypergraphes arbores, Discr. Math., 21 (1978), 223–227
R. Fagin, Degrees of acyclicity for hypergraphs and relational database schemes, Journal of the Assoc. for Comput. Mach., 30 (1983), 514–550
F. F. Dragan, C. F. Prisacaru, and V. D. Chepoi, Location problems in graphs and the Helly property (in Russian), Discrete Mathematics, Moscow, 4(1992), 67–73 (the full version appeared as preprint: F.F. Dragan, C.F. Prisacaru, and V.D. Chepoi, r-Domination and p-center problems on graphs: special solution methods and graphs for which this method is usable (in Russian), Kishinev State University, preprint Mo1dNIINTI, N. 948 - M88, 1987 )
M. Moscarini, Doubly chordal graphs, Steiner trees and connected domination, Networks, 23 (1993), 59–69
H. Behrendt and A. Brandstädt, Domination and the use of maximumneighbourhoods, Technical Report SM-DU-204, University of Duisburg 1992
A. Brandstädt, F.F. Dragan, V.D. Chepoi, and V.I. Voloshin, Dually chordal graphs, Technical Report SM-DU-225,University of Duisburg 1993, International Workshop on Graph-Theoretic Concepts in Computer Science WG’93, J. van Leeuwen (Ed.), 1993, Lecture Notes in Computer Science,to appear
J.L. Szwarcfiter and C.F. Bornstein, Clique graphs of chordal and path graphs, manuscript 1992, to appear in SIAM J. Discr. Math.
D.J. Rose, R.E. Tarjan, and G.S. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Computing, 5 (1976), 266–283
R.E. Tarjan and M. Yannakakis, Simple linear time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs, SIAM J. Computing 13, 3 (1984), 566–579
F.F. Dragan, HT-graphs: centers, connected r-domination and Steiner trees, manuscript 1992
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1994 B. G. Teubner Stuttgart
About this chapter
Cite this chapter
Brandstädt, A. (1994). Graphen und Hypergraphen mit Baumstruktur. In: Graphen und Algorithmen. Leitfäden und Monographien der Informatik. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-94689-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-322-94689-8_8
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-519-02131-5
Online ISBN: 978-3-322-94689-8
eBook Packages: Springer Book Archive