Abstract:In this note, we prove a tight lower bound on symmetric extended formulations for the spanning tree polytope of the complete graph. More precisely, let $P_{ST}(K_n)$ be the spanning tree polytope of $K_n$. We show that, for all $n\ge13$, every symmetric extended formulation for $P_{ST}(K_n)$ has at least $\binom n3$ inequalities. Since the classical Martin formulation has a symmetric formulation of size $O(n^3)$, this gives \[
\operatorname{xcs}(P_{ST}(K_n))=\Theta(n^3). \]
From: Sebastian Pokutta [view email]
[v1]
Mon, 15 Jun 2026 17:47:51 UTC (45 KB)
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