Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Smaller counterexamples to Hedetniemi's conjecture   Hedetniemi's conjecture~\cite{hedetniemi1966homomorphisms} for $c$-colorings
states that the tensor product $G \times H$ is $c$-colorable if and only if $G$
or $H$ is $c$-colorable. El-Zahar and Sauer~\cite{El-ZaharS85} proved it for $c
= 3$. In a recent breakthrough, Shitov~\cite{Shitov19} showed counterexamples,
for large $c$. While Shitov's proof is already remarkably short, Zhu
\cite{Zhu20} simplified the argument and gave a more explicit counterexample
for $c=125$. Tardif \cite{Tardif20} showed that a modification of the arguments
allows to use ``wide colorings'' to obtain counterexamples for $c=14$, and
$c=13$ with a more involved use of lexicographic products. This note presents
two more small modifications, resulting in counterexamples for $c=5$ (with $G$
and $H$ having 4686 and 30 vertices, respectively).

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn