
Extension Complexity of the Correlation Polytope
We prove that for every nvertex graph G, the extension complexity of th...
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Regular matroids have polynomial extension complexity
We prove that the extension complexity of the independence polytope of e...
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Local certification of graphs on surfaces
A proof labelling scheme for a graph class π is an assignment of certifi...
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Extended formulations for matroid polytopes through randomized protocols
Let P be a polytope. The hitting number of P is the smallest size of a h...
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LowCongestion Shortcuts for Graphs Excluding Dense Minors
We prove that any nnode graph G with diameter D admits shortcuts with c...
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Robust Connectivity of Graphs on Surfaces
Let Ξ(T) denote the set of leaves in a tree T. One natural problem is to...
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On classes of graphs with strongly sublinear separators
For real numbers c,epsilon>0, let G_c,epsilon denote the class of graphs...
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Smaller extended formulations for spanning tree polytopes in minorclosed classes and beyond
Let G be a connected nvertex graph in a proper minorclosed class π’. We prove that the extension complexity of the spanning tree polytope of G is O(n^3/2). This improves on the O(n^2) 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^3/2) bound for graphs embedded in a fixed surface. Our proof works more generally for all graph classes admitting strongly sublinear balanced separators: We prove that for every constant Ξ² with 0<Ξ²<1, if π’ is a graph class closed under induced subgraphs such that all nvertex graphs in π’ have balanced separators of size O(n^Ξ²), then the extension complexity of the spanning tree polytope of every connected nvertex graph in π’ is O(n^1+Ξ²). We in fact give two proofs of this result, one is a direct construction of the extended formulation, the other is via communication protocols. Using the latter approach we also give a short proof of the O(n) bound for planar graphs due to Williams (2002).
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