On the 2-chain subgraph cover and related problems

Journal of Algorithms

Volumn 17, Issue 2, 1994, Pages 251-268

  Ma, Tze Heng ^a   Spinrad, Jeremy P ^b  

^a INSTITUTE OF INFORMATION SCIENCE   (Taiwan)

^b VANDERBILT UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0005686062     PISSN: 01966774     EISSN: None     Source Type: Journal    
DOI: 10.1006/jagm.1994.1034     Document Type: Article

References (35)

1. K. A. Baker, P. C. Fishburn, and F. S. Roberts, Partial order of dimension 2, Networks 2 (1971), 11-28.
2. K. Bogart and W. T. Trotter, On the complexity of posets, Discrete Math. 16 (1976), 71-82.
3. A. Bouchet, "Etude Combinatoire des Ordonnes Finis—Applications, " These, Univer-site Scientifique et Medicale de Grenoble, 1971.
4. F. H. Cheah, "A Recognition Algorithm for Il-graphs, " Ph.D. thesis, Dept. of Computer Science, University of Toronto, 1990.
5. V. Chvatal and P. L. Hammer, "Set-packing and Threshold Graphs, " University of Waterloo Res. Report CORR 73-21, Waterloo, Ontario, Canada, 1973.
6. V. Chvatal and P. L. Hammer, Aggregation of inequalities in integer programming, in "Studies in Integer Programming, " Annals of Discrete Mathematics, Vol. 1 (P. L. Hammer et al., Eds.), pp. 145-162, North-Holland, Amsterdam, 1977.
7. D. G. Corneil and P. K. Kamula, Extensions of permutation and interval graphs, Congr. Numer. 58 (1987), 267-275.
8. O. Cogis, Ferrers digraphs and threshold graphs, Discrete Math. 38 (1982), 33-46.
9. O. Cogis, On the Ferrers dimension of a digraph, Discrete Math. 38 (1982), 47-52.
10. C. H. Coomb, "A Theory of Data, " Wiley, New York, 1964.
11. D. Coppersmith and S. Winograd, Matrix multiplication via arithmetic progressions, in "Proceedings, 19th Annual Symposium on the Theory of Computation, 1987, pp. 1-6.
12. M. B. Cozzens and M. D. Halsey, The relationship between the threshold dimension of split graphs and various dimensional parameters, Discrete Appl. Math. 30 (1991), 125-135.
13. R. M. Dawes, "Fundamentals of Attitude Measurement, " Wiley, New York, 1973.
14. J.-P. Doignon, A. Ducamp, and J.-C. Falmagne, On realizable biorders and the biorder dimension of a relation, J. Math. Psych. 28 (1984), 77-109.
15. I. Dagan, M. C. Golumbic, and R. Y. Pinter, Trapezoid graphs and their coloring, Discrete Appl. Math. 21 (1988), 35-46.
16. P. C. Fisiiburn, "Interval Orders and Interval Graphs, " Wiley, New York, 1985.
17. S. Foldes and P. Hammer, Split graphs, in "Proceedings, Eighth Southeastern Conf. Combinatorics, Graph Theory and Computing" (F. Hoffman et al., Eds.), pp. 311-315, Louisiana State University, Baton Rouge, LA, 1977.
18. M. C. Golumbic, "Algorithmic Graph Theory and Perfect Graphs, " Academic Press, New York, 1980.
19. C. P. Gabor, K. J. Supowit, and W.-L. Hsu, Recognizing circle graphs in polynomial time, J. Assoc. Comput. Mach. 36 (1989), 435-473.
20. A. J. Hoffman, A. W. J. Kolen, and M. Sakarovitch, Totally-balanced and greedy matrices, SIAM J. Algebraic Discrete Methods 6 (1985), 721-730.
21. M. Habib, D. Kelly, and R. H. Mohring, Interval dimension is a comparability invariant, Discrete Math. 88 (1991), 211-229.
22. P. L. Hammer, U. N. Pfled, and X. Sun, Difference graphs, Discrete Appl. Math. 28 (1990), 21-34.
23. M. Habib and R. H. Mohring, Recognition of partial orders with interval dimension two via transitive orientation with side constraints, preprint, 1989.
24. T. Ibaraki and U. N. Peled, Sufficient conditions for graphs to have threshold number 2, in "Studies on Graphs and Discrete Programming, " Annals of Discrete Mathematics, Vol. 11 (P. Hansen, Ed.), pp. 241-268, North-Holland, Amsterdam, 1981.
25. D. Kelly, The 3-irreducible partially ordered sets, Canad. J. Math. 29 (1977), 367-383.
26. A. Lubiw, Doubly lexical orderings of matrices, SIAM J. Comput. 16 (1987), 854-879.
27. C. H. Papadimitriou and M. Yannakakis, Scheduling interval-ordered tasks, SIAM J. Comput. 8 (1979), 405-409.
28. I. Rabinovitch and I. Rival, The rank of a distributive lattice, Discrete Math. 25 (1979), 275-279.
29. J. Spinrad, "Two Dimensional Partial Orders, " Ph.D. thesis, Princeton University, 1982.
30. J. Spinrad, On comparability and permutation graphs, SIAM J. Comput. 14 (1985), 658-670.
31. J. Spinrad, Doubly lexical ordering of dense 0-1 matrices, preprint, 1989.
32. A. Tucker, An efficient test for circular-arc graphs, SIAM J. Comput. 9 (1980), 1-24.
33. W. T. Trotter, Jr., and J. I. Moore, Characterization problems for graphs, partially ordered sets, lattices, and families of sets, Discrete Math. 16 (1976), 361-381.
34. M. Yannakakis, Computing the minimum fill-in is NP-complete, SIAM J. Algebraic Discrete Methods 1 (1981), 77-79.
35. M. Yannakakis, The complexity of the partial order dimension problem, SIAM J. Algebraic Discrete Methods 3 (1982), 351-358.