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Triangle-Freeness is Hard to Detect

Published online by Cambridge University Press:  21 November 2002

S. JUKNA  and
G. SCHNITGER
S. JUKNA
Affiliation:
Universität Frankfurt, Institut für Informatik, Robert-Mayer-Strasse 11-15, D-60054 Frankfurt, Germany (e-mail: jukna@thi.informatik.uni-frankfurt.de) Institute of Mathematics and Informatics, Akademijos 4, LT-2600 Vilnius, Lithuania
G. SCHNITGER
Affiliation:
Universität Frankfurt, Institut für Informatik, Robert-Mayer-Strasse 11-15, D-60054 Frankfurt, Germany (e-mail: jukna@thi.informatik.uni-frankfurt.de)
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Abstract

We show that recognizing the K3-freeness and K4-freeness of graphs is hard, respectively, for two-player nondeterministic communication protocols using exponentially many partitions and for nondeterministic syntactic read-r times branching programs.

The key ingredient is a generalization of a colouring lemma, due to Papadimitriou and Sipser, which says that for every balanced red—blue colouring of the edges of the complete n-vertex graph there is a set of εn2 triangles, none of which is monochromatic, such that no triangle can be formed by picking edges from different triangles. We extend this lemma to exponentially many colourings and to partial colourings.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 11 , Issue 6 , November 2002 , pp. 549 - 569
Copyright
2002 Cambridge University Press

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