Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Connectedness of Certain Graph Coloring Complexes   In this article, we consider the bipartite graphs $K_2 \times K_n$. We prove
that the connectedness of the complex $\displaystyle \text{Hom}(K_2\times
K_{n}, K_m) $ is $m-n-1$ if $m \geq n$ and $m-3$ in the other cases. Therefore,
we show that for this class of graphs, $\text{Hom} (G, K_m)$ is exactly $m-d-2$
connected, $m \geq n$, where $d$ is the maximal degree of the graph $G$.

12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn