Multipartite tournaments and the push operation
Date
1999
Authors
Wood, Kathryn L. B.
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Abstract
Given a digraph D and X ~ V(D), Dx is the digraph obtained from D by pushing X , that is, reversing the direction of all arcs with exactly one end in X . Recently, the study of this operation has been focussed on problems of characterizing digraphs which can be made to satisfy certain properties using the push operation. Klostermeyer proved that the problems of deciding whether a given digraph can be made acyclic, strong, Hamiltonian, or semi-connected, respectively, using the push operation are NP-complete.
In this thesis we characterize, in terms of forb idden structures, the multipartite tournaments that can be ma.de acyclic, ordinary, and unidirectional, respectively, using the push operation. We use our results to give a structural characterization of solvable instances of t he game 'Unbalancing Lights'. Finally, we present several characterizations of nearly-acyclic tournaments and the tournaments that can be made nearly-acyclic using the push operation. Our characterizations imply that the problems of deciding if a given multipartite tournament (respectively, tournament) can be made acyclic (respectively, nearly-acyclic) , ordinary, unidirectional, respectively, are solvable in polynomial time.