Best Odds for Finding a Perfect Matching in a Bipartite Graph

  • Authors:

  • W. Paulsen

  • Affiliations:

  • Department of Mathematics and Statistics, Arkansas State University, PO Box 70, State University, AR 72432, USA (e-mail: wpaulsen@math.astate.edu)

  • Venue:
  • Combinatorics, Probability and Computing
  • Year:
  • 2006

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Abstract

We will study the best way to reveal a hidden perfect matching in a balanced bipartite graph by eliminating edges, one by one, in the hope that the eliminated edge is not part of the mystery perfect matching. We will look for the strategy that maximizes the odds of finding the perfect matching without revealing a fixed number of the edges in that perfect matching. For a complete bipartite graph, this is equivalent to finding a mystery permutation via negative guesses with only a fixed number of incorrect negative guesses.