Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equitable partition of planar graphs   An equitable $k$-partition of a graph $G$ is a collection of induced
subgraphs $(G[V_1],G[V_2],\ldots,G[V_k])$ of $G$ such that
$(V_1,V_2,\ldots,V_k)$ is a partition of $V(G)$ and $-1\le |V_i|-|V_j|\le 1$
for all $1\le i<j\le k$. We prove that every planar graph admits an equitable
$2$-partition into $3$-degenerate graphs, an equitable $3$-partition into
$2$-degenerate graphs, and an equitable $3$-partition into two forests and one
graph.

22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga