Boxicity and poset dimension

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 6196 LNCS, Issue , 2010, Pages 3-12

  Adiga, Abhijin ^a   Bhowmick, Diptendu ^a   Chandran, L Sunil ^a  

^a INDIAN INSTITUTE OF SCIENCE   (India)

Author keywords

Boxicity; comparability graph; extended double cover; partial order; poset dimension

Indexed keywords

ANTI-SYMMETRIC; BIPARTITE GRAPHS; BOXICITY; CARTESIAN PRODUCTS; CHROMATIC NUMBER; COMPARABILITY GRAPHS; EDGE-SETS; FINITE GRAPHS; GRAPH G; INTERSECTION GRAPH; MAXIMAL ELEMENTS; MAXIMUM DEGREE; PARTIAL ORDER; POLYNOMIAL-TIME ALGORITHMS; TOTAL ORDER; TRANSITIVE BINARY RELATIONS; UPPER BOUND; VERTEX SET;

GRAPH THEORY;

EID: 77955027568     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-14031-0_3     Document Type: Conference Paper

References (26)

1. Bhowmick, D., Chandran, L.S.: Boxicity and cubicity of asteroidal triple free graphs. Disc. Math. 310, 1536-1543 (2010)
2. Chandran, L.S., Das, A., Shah, C.D.: Cubicity, boxicity, and vertex cover. Disc. Math. 309, 2488-2496 (2009)
3. Chandran, L.S., Francis, M.C., Mathew, R.: Chordal bipartite graphs with high boxicity. In: Japan conference on computation geometry and graphs, Kanazawa (2009)
4. Chandran, L.S., Francis, M.C., Sivadasan, N.: Boxicity and maximum degree. J. Combin. Theory Ser. B 98(2), 443-445 (2008)
5. Chandran, L.S., Sivadasan, N.: Boxicity and treewidth. J. Combin. Theory Ser. B 97(5), 733-744 (2007)
6. Chandran, L.S., Sivadasan, N.: The cubicity of hypercube graphs. Disc. Math. 308(23), 5795-5800 (2008)
7. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to algorithms. MIT press, Cambridge (2001)
8. Cozzens, M.B.: Higher and multi-dimensional analogues of interval graphs, Ph.D thesis, Department of Mathematics, Rutgers University, New Brunswick, NJ (1981)
9. Cozzens, M.B., Halsey, M.D.: The relationship between the threshold dimension of split graphs and various dimensional parameters. Disc. Appl. Math. 30, 125-135 (1991)
10. Dushnik, B., Miller, E.W.: Partially ordered sets. Amer. J. Math 6(3), 600-610 (1941)
11. Erdös, P., Kierstead, H., Trotter, W.T.: The dimension of random ordered sets. Random structures and algorithms 2, 253-275 (1991)
12. Esperet, L.: Boxicity of graphs with bounded degree. European J. Combin. 30(5), 1277-1280 (2009)
13. Fishburn, P.C.: Intransitive indifference with unequal indifference intervals. J. Math. Psych. 7, 144-149 (1983)
14. Füredi, Z., Kahn, J.: On the dimensions of ordered sets of bounded degree. Order 3, 15-20 (1986)
15. Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Academic Press, New York (1980)
16. Hegde, R., Jain, K.: The hardness of approximating poset dimension. Electronic Notes on Discrete Mathematics 29, 435-443 (2007)
17. Kratochvil, J.: A special planar satisfiability problem and a consequence of its NPcompleteness. Disc. Appl. Math. 52, 233-252 (1994)
18. Pnueli, A., Lempel, A., Even, S.: Transitive orientation of graphs and identification of permutation graphs. Canad. J. Math 23, 160-175 (1971)
19. Roberts, F.S.: On the boxicity and cubicity of a graph. In: Recent Progresses in Combinatorics, pp. 301-310. Academic Press, New York (1969)
20. Scheinerman, E.R.: Intersection classes and multiple intersection parameters, Ph.D. thesis, Princeton University (1984)
21. Thomassen, C.: Interval representations of planar graphs. J. Combin. Theory Ser. B 40, 9-20 (1986)
22. Trotter, W.T.: Dimension of the crown SKn . Disc. Math. 8, 85-103 (1974)
23. Trotter, W.T.: Combinatorics and partially ordered sets: Dimension Theory. The Johns Hopkins University Press, Baltimore (1992)
24. Trotter, W.T.: Graphs and partially ordered sets: recent results and new directions. In: Surveys in graph theory, San Fransisco, CA (1995), Congr. Numer. 116 (1996)
25. Trotter, W.T., Moore, J.I., Sumner, D.P.: The dimension of a comparability graph. Proc. Amer Math Soc. 60, 35-38 (1976)
26. Yannakakis, M.: The complexity of the partial order dimension problem. SIAM J. Alg. Disc. Math. 3(3), 351-358 (1982)