Vertex ranking of asteroidal triple-free graphs

Information Processing Letters

Volumn 68, Issue 4, 1998, Pages 201-206

  Kloks, Ton ^a   Müller, Haiko ^b   Wong, C K ^c  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Algorithms; Asteroidal triple free graph; Minimal separator; Vertex ranking

Indexed keywords

ALGORITHMS; POLYNOMIALS;

ASTEROIDAL TRIPLE-FREE GRAPH; MINIMAL SEPARATOR; VERTEX RANKING;

TREES (MATHEMATICS);

EID: 0042263930     PISSN: 00200190     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0020-0190(98)00162-8     Document Type: Article

References (18)

1. B. Aspvall, P. Heggernes, Finding minimum height elimination trees for interval graphs in polynomial time, BIT 34 (1994) 484-509.
2. H. Bodlaender, T. Kloks, D. Kratsch, Treewidth and pathwidth of permutation graphs, SIAM J. Discrete Math. 8 (1995) 606-616.
3. H. Bodlaender, J.S. Deogun, K. Jansen, T. Kloks, D. Kratsch, H. Müller, Z. Tuza, Rankings of graphs, SIAM J. Discrete Math. 11 (1998) 168-181.
4. A. Brandstädt, Special graph classes-a survey, Schriftenreihe des Fachbereichs Mathematik, SM-DU-199, Universität Duisburg Gesamthochschule, 1993.
5. D.G. Corneil, S. Olariu, L. Stewart, Asteroidal triple-free graphs, SIAM J. Discrete Math. 10 (1997) 399-430.
6. J.S. Deogun, T. Kloks, D. Kratsch, H. Müller, On vertex ranking for permutation and other graphs, in: 11th Annual Symposium on Theoretical Aspects of Computer Science, Lecture Notes in Comput. Sci., Vol. 775, Springer, Berlin, 1994, pp. 747-758.
7. I.S. Duff, J.K. Reid, The multifrontal solution of indefinite sparse symmetric linear equations, ACM Trans. Math. Software 9 (1983) 302-325.
8. M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
9. M. Katchalski, W. McCuaig, S. Seager, Ordered colourings, Discrete Math. 142 (1995) 141-154.
10. T. Kloks, D. Kratsch, Listing all minimal separators of a graph, SIAM J. Comput. 27 (1998) 605-613.
11. T. Kloks, D. Kratsch, H. Müller, Measuring the vulnerability for classes of intersection graphs, Discrete Appl. Math. 77 (1997) 259-270.
12. C.E. Leiserson, Area efficient graph layouts for VLSI, in: Proc. 21st Annual IEEE Symposium on Foundations of Computer Science, 1980, pp. 270-281.
13. C.G. Lekkerkerker, J.C. Boland Representation of a finite graph by a set of intervals on the real line, Fund. Math. 51 (1962) 45-64.
14. J.W.H. Liu, The role of elimination trees in sparse factorization, SIAM J. Matrix Anal. Appl. 11 (1990) 134-172.
15. A.A. Schäffer, Optimal node ranking of trees in linear time, Inform. Process. Lett. 33 (1989/90) 91-96.
16. P. Scheffler, Node ranking and searching on graphs (Abstract), in: U. Faigle and C. Hoede (Eds.), 3rd Twente Workshop on Graphs and Combinatorial Optimization, Memorandum No. 1132, Faculty of Applied Mathematics, University of Twente, The Netherlands, 1993.
17. A. Sen, H. Deng, S. Guha, On a graph partition problem with application to VLSI layout, Inform. Process. Lett. 43 (1992) 87-94.
18. M. Yannakakis, The complexity of the partial order dimension problem, SIAM J. Algebraic Discrete Methods 3 (1982) 351-358.