Abstract
In the study of extensions of polytopes of combinatorial optimization problems, a notorious open question is that for the size of the smallest extended formulation of the Spanning Tree polytope of a complete graph with n nodes. The best known lower bound is Ω(n2), the best known upper bound is O(n3).In this note we show that the venerable fooling set method cannot be used to improve the lower bound: every fooling set for the Spanning Tree polytope has size O(n2).
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