r-Dominating cliques in graphs with hypertree structure

Discrete Mathematics

Volumn 162, Issue 1-3, 1996, Pages 93-108

  Dragan, Feodor F ^a   Brandstädt, Andreas ^b  

^a MOLDOVA STATE UNIVERSITY   (Moldova)

^b UNIVERSITY OF ROSTOCK   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042041677     PISSN: 0012365X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0012-365X(95)00277-4     Document Type: Article

References (30)

1. H. Behrendt and A. Brandstädt, Domination and the use of maximum neighbourhoods, Tech. Report SM-DU-204, University of Duisburg, 1992.
2. C. Berge, Hypergraphs (North-Holland, Amsterdam, 1989).
3. A. Brandstädt, Special graph classes - a survey, Tech. Report SM-DU-199, University of Duisburg, 1993.
4. A. Brandstädt, V.D. Chepoi and F.F. Dragan, The algorithmic use of hypertree structure and maximum neighbourhood orderings, G. Tinhofer, E.W. Mayr and G. Schmidt, eds., Graph Theoretic Concepts in Computer Science, 20th Internat. Workshop WG '94, LNCS 903; 65-80.
5. A. Brandstädt, F.F. Dragan, V.D. Chepoi and V.I. Voloshin, Dually chordal graphs, Tech. Report SM-DU-225, University of Duisburg, 1993; in: J. van Leeuwen, ed, Graph Theoretic Concepts in Computer Science, 19th Internat. Workshop WG '93, Utrecht, The Netherlands, Lecture Notes in Computer Science, vol. 790 (Springer, Berlin, 1993) 237-251.
6. A. Brandstädt, F.F. Dragan, V.D. Chepoi and V.I. Voloshin, Dually chordal graphs, Tech. Report SM-DU-225, University of Duisburg, 1993; in: J. van Leeuwen, ed, Graph Theoretic Concepts in Computer Science, 19th Internat. Workshop WG '93, Utrecht, The Netherlands, Lecture Notes in Computer Science, vol. 790 (Springer, Berlin, 1993) 237-251.
7. A. Brandstädt and D. Kratsch, Domination problems on permutation and other graphs, Theoret. Comput. Sci. 54 (1987) 181-198.
8. G.J. Chang, Labeling algorithms for domination problems in sun-free chordal graphs, Discrete Appl. Math. 22 (1988/89) 21-34.
9. G.J. Chang and G.L. Nemhauser, The k-domination and k-stability problem on sun-free chordal graphs, SIAM J. Algebraic Discrete Methods 5 (1984) 332-345.
10. F.F. Dragan, Centers of graphs and the Helly property, Ph.D. Thesis, Moldova State University, 1989 (in Russian).
11. F.F. Dragan, Dominating and packing in triangulated graphs, (in Russian), Methods Discrete Anal. (Novosibirsk) (51) (1991) 17-36.
12. F.F. Dragan, Domination in Helly graphs without quadrangles, Cybernet. System Anal. (Kiev) (6) (1993) 47-57 (in Russian).
13. F.F. Dragan, HT-graphs: centers, connected r-domination and Steiner trees, Comput. Sci. J. Moldova (Kishinev) (2) (1993) 64-83.
14. F.F. Dragan, C.F. Prisacaru and V.D. Chepoi, r-Domination and p-center problems on graphs: special solution methods, Tech. Report Mold-NIINTI, N 948-M88, Kishinev State University, 1987 (in Russian).
15. F.F. Dragan, C.F. Prisacaru and V.D. Chepoi, Location problems in graphs and the Helly property, Diskretnaja Matematika (Moscow) 4 (4) (1992) 67-73 (in Russian).
16. P. Duchet, Propriete de Helly et problemes de representation, in: Colloqu. Intern. CNRS 260, Problemes Combin. et Theorie du Graphes, Orsay, France (1976) 117-118.
17. M. Farber, Domination, independent domination and duality in strongly chordal graphs, Discrete Appl. Math. 7 (1984) 115-130.
18. M. Farber and R.E. Jamison, Convexity in graphs and hypergraphs, SIAM J. Algebraic Discrete Methods 7 (1986) 433-444.
19. C. Flament, Hypergraphes arbores, Discrete Math. 21 (1978) 223-227.
20. M.C. Golumbic, Algorithmic Graph Theory and Perfect Graphs (Academic Press, New York, 1980).
21. R.B. Hayward, Weakly triangulated graphs, J. Combin Theory Ser. B 39 (1985) 200-208.
22. S.C. Hedetniemi and R. Laskar, eds., Topics on Domination, Ann. Discrete Math. 48 (North-Holland, Amsterdam, 1991).
23. D. Kratsch, Finding dominating cliques efficiently, in strongly chordal graphs and undirected path graphs, in: S.L. Hedetniemi and R.C. Laskar, eds., Topics on Domination, Ann. Discrete Math. 48 (North-Holland, Amsterdam, 1991) 225-238.
24. D. Kratsch, P. Damaschke and A. Lubiw, Dominating cliques in chordal graphs, Discrete Math. 128 (1994) 269-275.
25. M. Moscarini, Doubly chordal graphs, Steiner trees and connected domination, Networks 23 (1993) 59-69.
26. D.J. Rose, R.E. Tarjan and G.S. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput. (2) (1976) 266-283.
27. J.L. Szwarcfiter and C.F. Bornstein, Clique graphs of chordal and path graphs, Manuscript, 1992; SIAM J. Discrete Math. 7 (1994) 331-336.
28. J.L. Szwarcfiter and C.F. Bornstein, Clique graphs of chordal and path graphs, Manuscript, 1992; SIAM J. Discrete Math. 7 (1994) 331-336.
29. 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. Comput. 13 (3) (1984) 566-579.
30. V.I. Voloshin, On properties of triangulated graphs, Oper. Res. Programming (Kishinev) (1982) 24-32 (in Russian).