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The Feasible Matching Problem

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Abstract

Let G = (V, E) be a graph and \({R\subseteq E}\) . A matching M in G is called R-feasible if the subgraph induced by the M-saturated vertices does not have an edge of R. We show that the general problem of finding a maximum size R-feasible matching in G is NP-hard and identify several natural applications of this new concept. In particular, we use R-feasible matchings to give a necessary and sufficient condition for the existence of a systems of disjoint representatives in a family of hypergraphs. This provides another Hall-type theorem for hypergraphs. We also introduce the concept of R-feasible (vertex) cover and combine it with the concept of R-feasible matching to provide a new formulation and approach to Ryser’s conjecture.

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Authors and Affiliations

  1. Hunan University, Changsha, Hunan, 410082, China

    Yuejian Peng

  2. Indiana State University, Terre Haute, 47802, USA

    Yuejian Peng

  3. Mathematics Department, Illinois State University, Normal, IL, 61790-4520, USA

    Papa A. Sissokho

Authors
  1. Yuejian Peng
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  2. Papa A. Sissokho
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Correspondence to Yuejian Peng.

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Peng, Y., Sissokho, P.A. The Feasible Matching Problem. Graphs and Combinatorics 29, 695–704 (2013). https://doi.org/10.1007/s00373-012-1141-7

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  • DOI: https://doi.org/10.1007/s00373-012-1141-7

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