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On k-edge-connected Polyhedra: Box-TDIness in Series-Parallel Graphs

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Combinatorial Optimization (ISCO 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12176))

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Abstract

Given a connected graph \(G=(V,E)\) and an integer \(k\ge 1\), the connected graph \(H=(V,F)\), where F is a family of elements of E, is a k-edge-connected spanning subgraph of G if H remains connected after the removal of any \(k-1\) edges. The convex hull of the k-edge-connected spanning subgraphs of a graph G forms the k-edge-connected spanning subgraph polyhedron of G. We prove that this polyhedron is box-totally dual integral if and only if G is series-parallel. In this case, we also provide an integer box-totally dual integral system describing this polyhedron.

M. Barbato—While working on this paper, Michele Barbato was financially supported by Regione Lombardia, grant agreement n. E97F17000000009, project AD-COM.

R. Grappe—Supported by ANR DISTANCIA (ANR-17-CE40-0015).

M. Lacroix, E. Lancini and R. Grappe—This work has been partially supported by the PGMO project Matrices Totalement Équimodulaires.

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Acknowledgments

The authors wish to express their appreciation to the anonymous referees for their precious comments which helped to improve the presentation of the paper.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Milano, Milan, Italy

    Michele Barbato

  2. Université Sorbonne Paris Nord, LIPN, CNRS, UMR 7030, 93430, Villetaneuse, France

    Roland Grappe, Mathieu Lacroix & Emiliano Lancini

  3. Université Paris-Dauphine, PSL, LAMSADE, CNRS, UMR 7243, 75016, Paris, France

    Emiliano Lancini

Authors
  1. Michele Barbato
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  2. Roland Grappe
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  3. Mathieu Lacroix
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  4. Emiliano Lancini
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Corresponding author

Correspondence to Emiliano Lancini .

Editor information

Editors and Affiliations

  1. CNRS and Université Clermont Auvergne, Aubière, France

    Mourad Baïou

  2. Département d'informatique et de recherche opérationnelle & CIRRELT, University of Montreal, Montréal, QC, Canada

    Bernard Gendron

  3. School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, USA

    Oktay Günlük

  4. Laboratoire LAMSADE, Université Paris-Dauphine, Paris, France

    A. Ridha Mahjoub

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Barbato, M., Grappe, R., Lacroix, M., Lancini, E. (2020). On k-edge-connected Polyhedra: Box-TDIness in Series-Parallel Graphs. In: Baïou, M., Gendron, B., Günlük, O., Mahjoub, A.R. (eds) Combinatorial Optimization. ISCO 2020. Lecture Notes in Computer Science(), vol 12176. Springer, Cham. https://doi.org/10.1007/978-3-030-53262-8_3

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  • DOI: https://doi.org/10.1007/978-3-030-53262-8_3

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