Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hedetniemi's conjecture is asymptotically false   Extending a recent breakthrough of Shitov, we prove that the chromatic number
of the tensor product of two graphs can be a constant factor smaller than the
minimum chromatic number of the two graphs. More precisely, we prove that there
exists an absolute constant $\delta>0$ such that for all $c$ sufficiently
large, there exist graphs $G$ and $H$ with chromatic number at least
$(1+\delta)c$ for which $\chi(G \times H) \le c$.

31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th