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The chain graph sandwich problem

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Abstract

The chain graph sandwich problem asks: Given a vertex set V, a mandatory edge set E 1, and a larger edge set E 2, is there a graph G=(V,E) such that E 1⊆E⊆E 2 with G being a chain graph (i.e., a 2K 2-free bipartite graph)? We prove that the chain graph sandwich problem is NP-complete. This result stands in contrast to (1) the case where E 1 is a connected graph, which has a linear-time solution, (2) the threshold graph sandwich problem, which has a linear-time solution, and (3) the chain probe graph problem, which has a polynomial-time solution.

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Authors and Affiliations

  1. Instituto de Matemática, Universidade Federal Fluminense, Niterói, Rio de Janeiro, Brazil

    Simone Dantas

  2. COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Celina M. H. de Figueiredo

  3. Caesarea Rothschild Institute and Department of Computer Science, University of Haifa, Haifa, Israel

    Martin Charles Golumbic

  4. Instituto de Matemática and COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

    Sulamita Klein

  5. C.N.R.S., Laboratoire G-SCOP, Grenoble, France

    Frédéric Maffray

Authors
  1. Simone Dantas
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  2. Celina M. H. de Figueiredo
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  3. Martin Charles Golumbic
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  4. Sulamita Klein
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  5. Frédéric Maffray
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Corresponding author

Correspondence to Martin Charles Golumbic.

Additional information

This research was partially supported by CNPq, CAPES (Brazil)/COFECUB (France), FAPERJ.

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Dantas, S., de Figueiredo, C.M.H., Golumbic, M.C. et al. The chain graph sandwich problem. Ann Oper Res 188, 133–139 (2011). https://doi.org/10.1007/s10479-010-0792-0

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  • DOI: https://doi.org/10.1007/s10479-010-0792-0

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