Covering graphs with few complete bipartite subgraphs

Theoretical Computer Science

Volumn 410, Issue 21-23, 2009, Pages 2045-2053

  Fleischner, Herbert ^a   Mujuni, Egbert ^b   Paulusma, Daniël ^c   Szeider, Stefan ^c  

^a VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

^b UNIVERSITY OF DAR ES SALAAM   (Tanzania)

^c DURHAM UNIVERSITY   (United Kingdom)

Author keywords

Bicliques; Covering and partitioning problems; Parameterized complexity

Indexed keywords

BICLIQUE; BICLIQUES; BIPARTITE SUBGRAPHS; COMPUTATIONAL PROBLEMS; COVER PROBLEMS; COVERING AND PARTITIONING PROBLEMS; NP-COMPLETE; PARAMETERIZED COMPLEXITY; PARTITION PROBLEMS; VERTEX-COVER PROBLEMS;

GRAPH THEORY;

EID: 64249147833     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2008.12.059     Document Type: Article

References (24)

1. Amilhastre J., Vilarem M.C., and Janssen P. Complexity of minimum biclique cover and minimum biclique decomposition for bipartite domino-free graphs. Discrete Appl. Math. 86 2-3 (1998) 125-144
2. Chartrand G., and Lesniak L. Graphs & Digraphs. 4th edition (2005), Chapman & Hall/CRC, Boca Raton, FL
3. Cornaz D., and Fonlupt J. Chromatic characterization of biclique covers. Discrete Math. 306 5 (2006) 495-507
4. Dantas S., de Figueiredo C.M., Gravier S., and Klein S. Finding H-partitions efficiently. RAIRO - Theoret. Inform. Appl. 39 1 (2005) 133-144
5. Diestel R. Graph Theory. 2nd edition. Graduate Texts in Mathematics vol. 173 (2000), Springer-Verlag, New York
6. Downey R.G., and Fellows M.R. Parameterized Complexity. Monographs in Computer Science (1999), Springer-Verlag
7. Fishburn P.C., and Hammer P.L. Bipartite dimensions and bipartite degrees of graphs. Discrete Math. 160 (1996) 127-148
8. Flum J., and Grohe M. Parameterized Complexity Theory. Texts in Theoretical Computer Science. An EATCS Series vol. XIV (2006), Springer-Verlag
9. Garey M.R., and Johnson D.R. Computers and Intractability (1979), Freeman
10. Gramm J., Guo J., Hüffner F., and Niedermeier R. Data reduction, exact and heuristic algorithms for clique cover. Proc. ALENEX'06 (2006), SIAM 86-94
11. Gravier S., Kobler D., and Kubiak W. Complexity of list coloring problems with a fixed total number of colors. Discrete Appl. Math. 117 1-3 (2002) 65-79
12. Guo J., and Niedermeier R. Invitation to data reduction and problem kernelization. ACM SIGACT News 38 2 (2007) 31-45
13. M.H. Heydari, L. Morales, C.O. Shields Jr., I.H. Sudborough, Computing cross associations for attack graphs and other applications, in: 40th Hawaii International International Conference on Systems Science (HICSS-40 2007), 3-6 January 2007, Waikoloa, Big Island, HI, USA, 2007, pp. 270
14. Hüffner F., Niedermeier R., and Wernicke S. Techniques for practical fixed-parameter algorithms. J. Comput. 51 (2008) 7-25
15. Jiang T., and Ravikumar B. Minimal NFA Problems are hard. SIAM J. Comput. 22 (1993) 1117-1141
16. Lubiw A. The boolean basis problem and how to cover some polygons by rectangles. SIAM J. Discrete Math. 3 (1990) 98-115
17. E. Mujuni, F. Rosamond, Parameterized complexity of the clique partition problem, in: 14th Computing: The Australian Theory Symposium (CATS 2008), 22-25 January 2008, New South Wales, Australia, 2008, pp. 75-78
18. Müller H. On edge perfectness and classes of bipartite graphs. Discrete Math. 149 1-3 (1996) 159-187
19. Nau D.S., Markowsky G., Woodbury M.A., and Amos D.B. A mathematical analysis of human leukocyte antigen serology. Math. Biosci. 40 (1978) 243-270
20. Niedermeier R. Invitation to Fixed-Parameter Algorithms. Oxford Lecture Series in Mathematics and its Applications (2006), Oxford University Press
21. Orlin J. Contentment in graph theory: Covering graphs with cliques. Nederl. Akad. Wetensch. Proc. Ser. A 80, Indag. Math. 39 5 (1977) 406-424
22. L.J. Stockmeyer, The set basis problem is NP-complete, Technical Report RC-5431, IBM, 1975
23. Vikas N. Computational complexity of compaction to reflexive cycles. SIAM J. Comput. 32 1 (2002-2003) 253-280
24. Wille R. Restructuring lattice theory: An approach based on hierarchies of contexts. Ordered Sets. NATO ASI vol. 83 (1982), Reidel, Dordrecht, Holland 445-470