On the structure of graphs with bounded asteroidal number

Graphs and Combinatorics

Volumn 17, Issue 2, 2001, Pages 295-306

  Kloks, Ton ^a   Kratsch, Dieter ^b   Müller, Haiko ^b  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142190381     PISSN: 09110119     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003730170043     Document Type: Article

References (18)

1. Berry, A., Bordat, J.-P.: Separability generalizes Dirac's theorem. Discrete Appl. Math. 84, 43-53 (1998)
2. Broersma, H.J., Kloks, T., Kratsch, D., Müller, H.: Independent sets in asteroidal triple-free graphs. SIAM J. Discrete Math. 12, 267-287 (1999)
3. Broersma, H.J., Kloks, T., Kratsch, D., Müller, H.: A generalization of AT-free graphs and a generic algorithm for solving treewidth, minimum fill-in and vertex ranking. In: Lect. Notes Comput. Sci. 1517, Proceedings of WG'98, pp 88-99 Springer-Verlag, Berlin, Heidelberg, New York 1998
4. Cai, L., Corneil, D.G.: Tree spanners. SIAM J. Discrete Math. 8, 359-387 (1995)
5. Corneil, D.G., Olariu, S., Stewart, L.: Asteroidal triple-free graphs. SIAM J. Discrete Math. 10, 399-430 (1997)
6. Corneil, D.G., Olariu, S., Stewart, L.: Linear time algorithm for dominating pairs in asteroidal triple-free graphs. SIAM J. Comput. 28, 1284-1297 (1999)
7. Dirac, G.A.: On rigid circuit graphs. Abh. Math. Semin. Univ. Hamb. 25, 71-76 (1961)
8. Kloks, T., Kratsch, D.: Listing all minimal separators of a graph. SIAM J. Comput. 27, 605-613 (1998)
9. Kloks, T., Kratsch, D., Müller, H.: Asteroidal sets in graphs. In: Lect. Notes Comput. Sci. 1335, Proceedings of WG'97, pp 229-241 Berlin, Heidelberg, New York: Springer-Verlag 1997
10. Kloks, T., Kratsch, D., Spinrad, J.: On treewidth and minimum fill-in of asteroidal triple-free graphs. Theor. Comput. Sci. 175, 309-335 (1997)
11. Lekkerkerker, C.G., Boland, J.Ch.: Representation of a finite graph by a set of intervals on the real line. Fundam. Math. 51, 45-64 (1962)
12. Lin, I.J., McKee, T.A., West, D.B.: Leafage of chordal graphs. Discuss. Math. Graph Th. 18, 23-48 (1998)
13. Möhring, R.H.: Computationally tractable classes of ordered sets. In: I. Rival: Algorithms and Orders, pp 105-193, Dordrecht: Kluwer Academic Publishers 1989
14. Möhring, R.H.: Triangulating graphs without asteroidal triples. Discrete Appl. Math. 64, 281-287 (1996)
15. Parra, A.: Structural and algorithmic aspects of chordal graph embeddings. PhD. thesis, Technische Universität Berlin, Germany 1996
16. Prisner, E.: Representing triangulated graphs in stars. Abh. Math. Semin. Univ. Hamb. 62, 29-41 (1992)
17. Prisner, E.: Distance approximating spanning trees. In: Lect. Notes Comput. Sci. 1200, Proceedings of STACS'97, pp 499-510 Springer-Verlag 1997
18. Walter, J.R.: Representations of chordal graphs as subtrees of a tree. J. Graph Theory 2, 265-267 (1978)