Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linear colorings of simplicial complexes and collapsing   A vertex coloring of a simplicial complex $\Delta$ is called a linear
coloring if it satisfies the property that for every pair of facets $(F_1,
F_2)$ of $\Delta$, there exists no pair of vertices $(v_1, v_2)$ with the same
color such that $v_1\in F_1\backslash F_2$ and $v_2\in F_2\backslash F_1$. We
show that every simplicial complex $\Delta$ which is linearly colored with $k$
colors includes a subcomplex $\Delta'$ with $k$ vertices such that $\Delta'$ is
a strong deformation retract of $\Delta$. We also prove that this deformation
is a nonevasive reduction, in particular, a collapsing.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con