Recognizing graphs without asteroidal triples

Journal of Discrete Algorithms

Volumn 2, Issue 4, 2004, Pages 439-452

  Köhler, Ekkehard ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Asteroidal triple free graphs; Graph algorithms; Knotting graph; Recognition algorithm

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; MATRIX ALGEBRA; PROBLEM SOLVING; REAL TIME SYSTEMS; THEOREM PROVING;

ASTEROIDAL TRIPLE-FREE GRAPHS; GRAPH ALGORITHMS; KNOTTING GRAPH; RECOGNITION ALGORITHMS;

GRAPH THEORY;

EID: 9644270478     PISSN: 15708667     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jda.2004.04.005     Document Type: Article

References (21)

1. N. Alon, R. Yuster, U. Zwick, Finding and counting given length cycles, Algorithmica 17 (3) (1997) 209-223.
2. S. Booth, G.S. Lueker, Testing for the consecutive ones property, interval graphs, and planarity using PQ-tree algorithms, J. Comput. System Sci. 13 (1976) 335-379.
3. D.G. Corneil, S. Olariu, L. Stewart, The ultimate interval graph recognition algorithm?, in: Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, 1998, pp. 175-180.
4. D.G. Corneil, S. Olariu, L. Stewart, Linear time algorithms for dominating pairs in asteroidal triple-free graphs, SIAM J. Comput. 28 (4) (1999) 1284-1297.
5. P. Damaschke, Forbidden ordered subgraphs, in: R. Bodendiek, R. Henn (Eds.), Topics in Combinatorics and Graph Theory, Physica-Verlag, Heidelberg, 1990, pp. 219-229.
6. D.R. Fulkerson, O.A. Gross, Incidence matrices and interval graphs, Pacific J. Math. 15 (1965) 835-855.
7. H. Gabow, Private communication, 1994.
8. T. Gallai, Transitiv orientierbare Graphen, Acta Math. Acad. Sci. Hungar. 18 (1967) 25-66.
9. P.C. Gilmore, A.J. Hoffman, A characterization of comparability graphs and of interval graphs, Canad. J. Math. 16 (1964) 539-548.
10. M.Ch. Golumbic, C.L. Monma, W.T. Trotter, Tolerance graphs, Discrete Appl. Math. 9 (1984) 157-170.
11. H. Hempel, D. Kratsch, On claw-free asteroidal triple-free graphs, in: P. Widmayer (Ed.), Proceedings of the 25th International Workshop on Graph-Theoretic Concepts in Computer Science (WG'99), in: Lecture Notes in Comput. Sci., vol. 1665, 1999, pp. 377-390.
12. H. Ito, M. Yokoyama, Linear time algorithms for graph search and connectivity determination on complement graphs, Inform. Process. Lett. 66 (1998) 209-213.
13. D. Kelly, Comparability graphs, in: I. Rival (Ed.), Graphs and Order, Reidel, Dordrecht, 1985, pp. 3-40.
14. E. Köhler, Graphs without asteroidal triples, Ph.D. Thesis, Technische Universität Berlin, Cuvillier Verlag, Göttingen, 1999.
15. C.G. Lekkerkerker, J.Ch. Boland, Representation of a finite graph by a set of intervals on the real line, Fund. Math. 51 (1962) 45-64.
16. R. McConnell, Private communication, 1996.
17. R.H. Möhring, Triangulating graphs without asteroidal triples, Discrete Appl. Math. 64 (3) (1996) 281-287.
18. A. Parra, Structural and algorithmic aspects of chordal graph embeddings, Ph.D. Thesis, Technical University, Berlin, 1996.
19. G. Ramalingham, C. Pandu Rangan, A unified approach to domination problems in interval graphs, Inform. Process. Lett. 27 (1988) 271-274.
20. D.J. Rose, R.E. Tarjan, G.S. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput. 5 (1976) 266-283.
21. J.P. Spinrad, Efficient Graph Representations, in: Field Institute Monographs, vol. 79, American Mathematical Society, 2003.