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Three Equivalent Partial Orders on Graphs with Real Edge-Weights Drawn on a Convex Polygon

  • Hiro Ito
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3742)

Abstract

Three partial orders, cut-size order, length order, and operation order, defined between labeled multigraphs with the same order are known to be equivalent. This paper extends the result on edge-capacitated graphs, where the capacities are real numbers, and it presents a proof of the equivalence of the three relations. From this proof, it is also shown that we can determine whether or not a given graph precedes another given graph in polynomial time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hiro Ito
    • 1
  1. 1.Department of Communications and Computer Engineering, School of InformaticsKyoto UniversityKyotoJapan

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