Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-30T01:54:15.358Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Number of 2-SAT Functions

Published online by Cambridge University Press:  01 September 2009

L. ILINCA  and
J. KAHN
L. ILINCA
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA (e-mail: [email protected], [email protected])
J. KAHN
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA (e-mail: [email protected], [email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We give an alternative proof of a conjecture of Bollobás, Brightwell and Leader, first proved by Peter Allen, stating that the number of Boolean functions definable by 2-SAT formulae is . One step in the proof determines the asymptotics of the number of ‘odd-blue-triangle-free’ graphs on n vertices.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 18 , Issue 5: New Directions in Algorithms, Combinatorics and Optimization , September 2009 , pp. 749 - 764
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Allen, P. (2007) Almost every 2-SAT function is unate. Israel J. Math. 161 311–346.CrossRefGoogle Scholar
[2]Bollobás, B., Brightwell, G. and Leader, I. (2003) The number of 2-SAT functions. Israel J. Math. 133 45–60.CrossRefGoogle Scholar
[3]Brightwell, G. (2008) Personal communication.Google Scholar
[4]Erdős, P., Kleitman, D. J. and Rothschild, B. L. (1976) Asymptotic enumeration of Kn-free graphs. In Colloquio Internazionale sulle Teorie Combinatorie (Rome 1973), Vol. II, Accad. Naz. Lincei, Rome, pp. 19–27.Google Scholar
[5]Kleitman, D. J. and Rothschild, B. L. (1975) Asymptotic enumeration of partial orders on a finite set. Trans. Amer. Math. Soc. 205 205–220.CrossRefGoogle Scholar
[6]Prömel, H. J., Schickinger, T. and Steger, A. (2002) A note on triangle-free and bipartite graphs. Discrete Math. 257 531–540.CrossRefGoogle Scholar
[7]Szemerédi, E. (1978) Regular partitions of graphs. In Problèmes Combinatoires et Théorie des Graphes (Colloq. Internat. CNRS, Orsay 1976), CNRS, Paris, pp. 399–401.Google Scholar