Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A relative of Hadwiger's conjecture   Hadwiger's conjecture asserts that if a simple graph $G$ has no $K_{t+1}$
minor, then its vertex set $V(G)$ can be partitioned into $t$ stable sets. This
is still open, but we prove under the same hypotheses that $V(G)$ can be
partitioned into $t$ sets $X_1,\ldots, X_t$, such that for $1\le i\le t$, the
subgraph induced on $X_i$ has maximum degree at most a function of $t$. This is
sharp, in that the conclusion becomes false if we ask for a partition into
$t-1$ sets with the same property.

20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat