Fork-forests in bi-colored complete bipartite graphs

  • Authors:

  • Maria Axenovich;Marcus Krug;Georg Osang;Ignaz Rutter

  • Affiliations:

  • Departments of Mathematics, Iowa State University, USA and Karlsruhe Institute of Technology, Germany;Faculty of Informatics, Karlsruhe Institute of Technology, Germany;Karlsruhe Institute of Technology, Germany;Faculty of Informatics, Karlsruhe Institute of Technology, Germany

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2013

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Abstract

Motivated by the problem in (Tveretina et al., 2009) [8], which studies problems from propositional proof complexity, 2-edge colorings of complete bipartite graphs are investigated. It is shown that if the edges of G=K"n","n are colored with black and white such that the number of black edges differs from the number of white edges by at most 1, then there are at least n(1-1/2) vertex-disjoint forks with centers in the same partite set of G. Here, a fork is a graph formed by two adjacent edges of different colors. The bound is sharp. Moreover, an algorithm running in time O(n^2lognn@a(n^2,n)logn) and giving a largest such fork forest is found.