On the powers of graphs with bounded asteroidal number

Discrete Mathematics

Volumn 223, Issue 1-3, 2000, Pages 125-133

  Ho, Ting Yem ^a,c   Chang, Jou Ming ^b,c   Wang, Yue Li ^a  

^a NATIONAL TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Taiwan)

^b NATIONAL CENTRAL UNIVERSITY   (Taiwan)

^c NATIONAL TAIPEI UNIVERSITY OF BUSINESS   (Taiwan)

Author keywords

Asteroidal triple; AT free graphs; Powers of graphs; Strong perfect graph conjecture

Indexed keywords

EID: 0142221568     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-365X(00)00043-1     Document Type: Article

References (24)

1. H.-J. Bandelt, A. Henkmann, F. Nicolai, Powers of distance-hereditary graphs, Discrete Math. 145 (1995) 37-60.
2. C. Berge, Les problèmes de coloration en theéorie des graphes, Publ. Inst. Statist. Univ. Paris 9 (1960) 123-160.
3. C. Berge, V. Chvátal (Eds.), Topics on Perfect Graphs, Annals of Discrete Mathematics, Vol. 21, North-Holland, Amsterdam, 1984.
4. A. Brandstädt, F.F. Dragan, V.D. Chepoi, V.I. Voloshin, Dually chordal graphs, SIAM J. Discrete Math. 11 (1998) 437-455.
5. A. Brandstädt, V.B. Le, J.P. Spinrad, Graph Classes: A Survey (series) SIAM Monographs on Discrete Mathematics and Applications, SIAM, Philadelphia, PA, 1999.
6. A. Brandstädt, V.B. Le, T. Szymczak, Duchet-type theorems for powers of HHD-free graphs, Discrete Math. 177 (1997) 9-16.
7. H. Broersma, T. Kloks, D. Kratsch, H. Muller, Independent sets in asteroidal triple-free graphs, SIAM J. Discrete Math. 12 (1999) 267-287.
8. F. Cheah, A recognition algorithm for II - graphs, Doctoral thesis, Department of Computer Science, University of Toronto, 1990.
9. D.G. Corneil, S. Olariu, L. Stewart, A linear time algorithm to compute a dominating path in an AT-free graph, Inform. Process. Lett. 54 (1995) 253-257.
10. D.G. Corneil, S. Olariu, L. Stewart, Asteroidal triple-free graphs, SIAM J. Discrete Math. 10 (1997) 399-430.
11. D.G. Corneil, S. Olariu, L. Stewart, Linear time algorithms for dominating pairs in asteroidal triple-free graphs, SIAM J. Comput. 28 (1999) 1284-1297.
12. E. Dahlhaus, P. Duchet, On strongly chordal graphs, Ars Combin. 24B (1987) 23-30.
13. P. Damaschke, Distances in cocomparability graphs and their powers, Discrete Appl. Math. 35 (1992) 67-72.
14. P. Duchet, Classical perfect graphs, Ann. Discrete Math. 21 (1984) 67-96.
15. C. Flotow, On powers of m-trapezoid graphs, Discrete Appl. Math. 63 (1995) 187-192.
16. M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs, Academic Press, New York, 1980.
17. T. Kloks, D. Kratsch, H. Müller, Asteroidal sets in graph, in: Proc. of WG'97 Conference, Lecture Notes in Computer Science, Vol. 1335, Springer, New York, 1997, pp. 229-241.
18. T. Kloks, D. Kratsch, J. Spinrad, On treewidth and minimum fill-in of asteroidal triple-free graphs, Theoret. Comput. Sci. 175 (1997) 309-335.
19. 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.
20. A. Lubiw, T-free matrices, M.S. Thesis, Department of Combinatorics and Optimization, University of Waterloo, 1982.
21. R.H. Möhring, Triangulating graphs without asteroidal triples, Discrete Appl. Math. 64 (1996) 281-287.
22. A. Raychaudhuri, On powers of interval and unit interval graphs, Congr. Numer. 59 (1987) 235-242.
23. A. Raychaudhuri, On powers of strongly chordal and circular arc graphs, Ars Combin. 34 (1992) 147-160.
24. J.R. Walter, Representations of chordal graphs as subtrees of a tree, J. Graph Theory 2 (1978) 265-267.