Conservative weightings and eardecompositions of graphs
 András Frank
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A subsetJ of edges of a connected undirected graphG=(V, E) is called ajoin if C∩J≤C/2 for every circuitC ofG. Answering a question of P. Solé and Th. Zaslavsky, we derive a minmax 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 factorcritical graph.
To study these parameters we introduce a new decomposition ofG, interesting for its own sake, whose building blocks are factorcritical graphs and matchingcovered 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 GallaiEdmonds structure theorem and gives rise to a polynomial time algorithm to construct the optima in question.
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 Title
 Conservative weightings and eardecompositions of graphs
 Journal

Combinatorica
Volume 13, Issue 1 , pp 6581
 Cover Date
 19930301
 DOI
 10.1007/BF01202790
 Print ISSN
 02099683
 Online ISSN
 14396912
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 05 C 70
 05 C 75
 94 B 60
 Industry Sectors
 Authors

 András Frank ^{(1)} ^{(2)}
 Author Affiliations

 1. Department of Computer Science, Eötvös University, Múzeum krt. 68, H1088, Budapest, Hungary
 2. Institute for Operations Research, University of Bonn, Nassestr. 2, D5300, Bonn1, Germany