Conservative weightings and ear-decompositions 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 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.
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- Conservative weightings and ear-decompositions of graphs
Volume 13, Issue 1 , pp 65-81
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- András Frank (1) (2)
- Author Affiliations
- 1. Department of Computer Science, Eötvös University, Múzeum krt. 6-8, H-1088, Budapest, Hungary
- 2. Institute for Operations Research, University of Bonn, Nassestr. 2, D-5300, Bonn-1, Germany