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A constructive proof that tree are well-quasi-ordered under minors (detailed abstract)

  • Arvind Gupta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 620)

Abstract

The recent proof of Robertson and Seymour that graphs are well-quasi-ordered under minors immediately implies that a number of intesting problems have polynomial time algorithms. However, partially because of their non-constructive nature, these proofs do not yield any information about the algorithms. Here we present a constructive proof that trees are well-quasi-ordered under minors. This extends the results of Murty and Russell [MR90] who give a constructive proof of Higman's Lemma. Our proof is based on transforming finite sequences of trees to ordinals. We begin by describing a transformation which carries trees to finite strings of numbers and give an ordering on these strings which preserves the minor ordering on the underlying trees. We show that in our well-quasi-ordering argument, these strings are actually over a finite alphabet. This allows us to conclude the result. We require the well-ordering of the ordinal ε0 for our proof.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Arvind Gupta
    • 1
  1. 1.School of Computing ScienceSimon Fraser UniversityBurnabyCanada

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