Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smaller extended formulations for spanning tree polytopes in
  minor-closed classes and beyond   Let $G$ be a connected $n$-vertex graph in a proper minor-closed class
$\mathcal G$. 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 $\beta$ with $0<\beta<1$, if $\mathcal G$ is a graph class
closed under induced subgraphs such that all $n$-vertex graphs in $\mathcal G$
have balanced separators of size $O(n^\beta)$, then the extension complexity of
the spanning tree polytope of every connected $n$-vertex graph in $\mathcal{G}$
is $O(n^{1+\beta})$. 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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The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
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The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org