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Computing the independence number of dense triangle-free graphs

  • Stephan Brandt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1335)

Abstract

Computing the independence number of a graph remains NP-hard, even restricted to the class of triangle-free graphs. So the question arises, whether this remains valid if the minimum degree is required to be large. While in general graphs this problem remains NP-hard even within the class of graphs with minimum degree δ > (1 − ε)n, the situation is different for triangle-free graphs. It will be shown that for triangle-free graphs with δ > n/3 the independence number can be computed as fast as matrix multiplication, while within the class of triangle-free graphs with δ > (1-ε)n/4 the problem is already NP-hard.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Stephan Brandt
    • 1
  1. 1.FB Mathematik & Informatik, WE 2Freie Universität BerlinBerlinGermany

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