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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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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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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