Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cops, Robbers, and Threatening Skeletons: Padded Decomposition for
  Minor-Free Graphs   We prove that any graph excluding $K_r$ as a minor has can be partitioned
into clusters of diameter at most $\Delta$ while removing at most $O(r/\Delta)$
fraction of the edges. This improves over the results of Fakcharoenphol and
Talwar, who building on the work of Klein, Plotkin and Rao gave a partitioning
that required to remove $O(r^2/\Delta)$ fraction of the edges.
  Our result is obtained by a new approach to relate the topological properties
(excluding a minor) of a graph to its geometric properties (the induced
shortest path metric). Specifically, we show that techniques used by Andreae in
his investigation of the cops-and-robbers game on excluded-minor graphs can be
used to construct padded decompositions of the metrics induced by such graphs.
In particular, we get probabilistic partitions with padding parameter $O(r)$
and strong-diameter partitions with padding parameter $O(r^2)$ for $K_r$-free
graphs, padding $O(k)$ for graphs with treewidth $k$, and padding $O(\log g)$
for graphs with genus $g$.

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The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
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The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol