Combinatorica

, Volume 13, Issue 1, pp 65–81

Conservative weightings and ear-decompositions of graphs

  • András Frank
Article
  • 194 Downloads

Abstract

A subsetJ of edges of a connected undirected graphG=(V, E) is called ajoin if |CJ|≤|C|/2 for every circuitC ofG. Answering a question of P. Solé and Th. Zaslavsky, we derive a min-max formula for the maximum cardinality μ of a joint ofG. Namely, μ=(φ+|V|−1)/2 where φ denotes the minimum number of edges whose contraction leaves a factor-critical graph.

To study these parameters we introduce a new decomposition ofG, interesting for its own sake, whose building blocks are factor-critical graphs and matching-covered bipartite graphs. We prove that the length of such a decomposition is always φ and show how an optimal join can be constructed as the union of perfect matchings in the building blocks. The proof relies on the Gallai-Edmonds structure theorem and gives rise to a polynomial time algorithm to construct the optima in question.

AMS subject classification code (1991)

05 C 70 05 C 75 94 B 60 

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Copyright information

© Akadémiai Kiadó 1993

Authors and Affiliations

  • András Frank
    • 1
    • 2
  1. 1.Department of Computer ScienceEötvös UniversityBudapestHungary
  2. 2.Institute for Operations ResearchUniversity of BonnBonn-1Germany

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