Maximum directed cuts in acyclic digraphs

  • Authors:

  • Noga Alon;Béla Bollobás;András Gyárfás;Jenő Lehel;Alex Scott

  • Affiliations:

  • Schools of Mathematics and Computer Science, Raymond and Beverly Sackler, Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel and IAS, Princeton, NJ 08540;Trinity College, Cambridge CB2 1TQ, UK and Department of Mathematical Sciences, University of Memphis, Memphis TN38152;Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, P. O. Box 63, 1518, Hungary;Department of Mathematical Sciences, University of Memphis, Memphis TN38152 and Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, P. O. Box 63, 1518, Hungary;Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2007

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Abstract

It is easily shown that every digraph with m edges has a directed cut of size at least m-4, and that 1-4 cannot be replaced by any larger constant. We investigate the size of the largest directed cut in acyclic digraphs, and prove a number of related results concerning cuts in digraphs and acyclic digraphs. © 2006 Wiley Periodicals, Inc. J Graph Theory 55: 1–13, 2007