Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quickly excluding a non-planar graph   A cornerstone theorem in the Graph Minors series of Robertson and Seymour is
the result that every graph $G$ with no minor isomorphic to a fixed graph $H$
has a certain structure. The structure can then be exploited to deduce
far-reaching consequences. The exact statement requires some explanation, but
roughly it says that there exist integers $k,n$ depending on $H$ only such that
$0<k<n$ and for every $n\times n$ grid minor $J$ of $G$ the graph $G$ has a a
$k$-near embedding in a surface $\Sigma$ that does not embed $H$ in such a way
that a substantial part of $J$ is embedded in $\Sigma$. Here a $k$-near
embedding means that after deleting at most $k$ vertices the graph can be drawn
in $\Sigma$ without crossings, except for local areas of non-planarity, where
crossings are permitted, but at most $k$ of these areas are attached to the
rest of the graph by four or more vertices and inside those the graph is
constrained in a different way, again depending on the parameter $k$.
  The original and only proof so far is quite long and uses many results
developed in the Graph Minors series. We give a proof that uses only our
earlier paper [A new proof of the flat wall theorem, {\it J.~Combin.\ Theory
Ser.\ B \bf 129} (2018), 158--203] and results from graduate textbooks.
  Our proof is constructive and yields a polynomial time algorithm to construct
such a structure. We also give explicit constants for the structure theorem,
whereas the original proof only guarantees the existence of such constants.

9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph