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Abstract

Consider the following one player game on an empty graph with n vertices. The edges are presented one by one to the player in a random order. One of two colors, red or blue, has to be assigned to each edge immediately. The player’s object is to color as many edges as possible without creating a monochromatic clique K of some fixed size ℓ. We prove a threshold phenomenon for the expected duration of this game. We show that there is a function N 0 = N 0(ℓ, n) such that the player can asymptotically almost surely survive up to N(n) ≪ N 0 edges by playing greedily and that this is best possible, i.e., there is no strategy such that the game would last for N(n) ≫ N 0 edges.

Keywords

Random Graph Graph Property Edge Coloring Base Graph Greedy Strategy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Martin Marciniszyn
    • 1
  • Reto Spöhel
    • 1
  • Angelika Steger
    • 1
  1. 1.Institute of Theoretical Computer ScienceETH ZürichZürichSwitzerland

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