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The facets of the spanning trees polytope

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Abstract

Let \(G=(V, E)\) be an undirected graph. The spanning trees polytope P(G) is the convex hull of the characteristic vectors of all spanning trees of G. In this paper, we describe all facets of P(G) as a consequence of the facets of the bases polytope P(M) of a matroid M, i.e., the convex hull of the characteristic vectors of all bases of M.

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Acknowledgements

The author is grateful to Smail Djebali and anonymous referees for their valuable remarks in a previous version of this paper.

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  1. Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh, 11623, Saudi Arabia

    Brahim Chaourar

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  1. Brahim Chaourar
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Correspondence to Brahim Chaourar.

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Chaourar, B. The facets of the spanning trees polytope. Math Meth Oper Res 96, 113–121 (2022). https://doi.org/10.1007/s00186-022-00786-w

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  • DOI: https://doi.org/10.1007/s00186-022-00786-w

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