Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reducing quadrangulations of the sphere and the projective plane   We show that every quadrangulation of the sphere can be transformed into a
$4$-cycle by deletions of degree-$2$ vertices and by $t$-contractions at
degree-$3$ vertices. A $t$-contraction simultaneously contracts all incident
edges at a vertex with stable neighbourhood. The operation is mainly used in
the field of $t$-perfect graphs. We further show that a non-bipartite
quadrangulation of the projective plane can be transformed into an odd wheel by
$t$-contractions and deletions of degree-$2$ vertices. We deduce that a
quadrangulation of the projective plane is (strongly) $t$-perfect if and only
if the graph is bipartite.

28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th