Combinatorica

, Volume 16, Issue 3, pp 417–431 | Cite as

Orthogonal representations over finite fields and the chromatic number of graphs

  • René Peeters
Article

Abstract

We study the relationship between the minimum dimension of an orthogonal representation of a graph over a finite field and the chromatic number of its complement. It turns out that for some classes of matrices defined by a graph the 3-colorability problem is equivalent to deciding whether the class defined by the graph contains a matrix of rank 3 or not. This implies the NP-hardness of determining the minimum rank of a matrix in such a class. Finally we give for any class of matrices defined by a graph that is interesting in this respect a reduction of the 3-colorability problem to the problem of deciding whether or not this class contains a matrix of rank equal to three.

Mathematics Subject Classification (1991)

05C15 05C20 

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Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • René Peeters
    • 1
  1. 1.Department of EconometricsTilburg University5000 LETilburg

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