Abstract
In 1987, Nešetřil and Rödl [4] claimed to have proved that the problem of finding whether a given graphG can be oriented as the diagram of a partial order is NP-complete. A flaw was discovered in their proof by Thostrup [11]. Nešetřil and Rödl [5] have since corrected the proof, but the new version is rather complex. We give a simpler and more elementary proof, using a completely different approach.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
M. R. Garey and D. S. Johnson (1979)Computers and Intractability: A Guide to the Theory of NP-completeness, Freeman.
C. Lund and M. Yannakakis (1993) On the hardness of approximating minimization problems, in25th ACM Symposium on the Theory of Computing, pp. 286–293.
K. M. Mosesian (1972) Certain theorems on strongly basable graphs [Russian],Akad. Nauk Armian. SSR Dokl. 55, 83–86.
J. Nešetřil and V. Rödl (1987) Complexity of diagrams,Order 3, 321–330.
J. Nešetřil and V. Rödl, More on complexity of diagrams, submitted toOrder.
O. Ore (1962)Theory of Graphs, AMS Coll. Publ.34, Providence, RI.
O. Pretzel (1985) On graphs that can be oriented as diagrams of ordered sets,Order 2, 25–40.
O. Pretzel (1986) On reorienting graphs by pushing down maximal vertices,Order 3, 135–153.
O. Pretzel (1986) Orientations and reorientations of graphs,Cont. Math. 57, 103–125.
O. Pretzel and D. Youngs (1991) Balanced graphs and noncovering graphs,Disc. Math. 88, 279–287.
J. Thostrup (1992) Partial ordered sets and graphs (in Danish), MSc. dissertation, Odense University, Denmark, 56 pp.
Author information
Authors and Affiliations
Additional information
Communicated by I. Rival
Rights and permissions
About this article
Cite this article
Brightwell, G. On the complexity of diagram testing. Order 10, 297–303 (1993). https://doi.org/10.1007/BF01108825
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01108825