Corpus ID: 235592790

# Smaller extended formulations for spanning tree polytopes in minor-closed classes and beyond

@article{Aprile2021SmallerEF,
title={Smaller extended formulations for spanning tree polytopes in minor-closed classes and beyond},
author={Manuel Aprile and Samuel Fiorini and Tony Huynh and Gwena{\"e}l Joret and David R. Wood},
journal={ArXiv},
year={2021},
volume={abs/2106.11945}
}
Let G be a connected n-vertex graph in a proper minor-closed class G. We prove that the extension complexity of the spanning tree polytope of G is O(n). This improves on the O(n) bounds following from the work of Wong (1980) and Martin (1991). It also extends a result of Fiorini, Huynh, Joret, and Pashkovich (2017), who obtained a O(n) bound for graphs embedded in a fixed surface. Our proof works more generally for all graph classes admitting strongly sublinear balanced separators: We prove… Expand
1 Citations
Extended formulations for matroid polytopes through randomized protocols
It is shown that, if P is the base polytope of any matroid, then P admits an extended formulation whose size depends linearly on the hitting number of P, which is the smallest size of a hitting set of the facets of P. Expand

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