Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Equivalent Color Transform and Four Coloring Theorem   In this paper, we apply an equivalent color transform (ECT) for a minimal
$k$-coloring of any graph $G$. It contracts each color class of the graph to a
single vertex and produces a complete graph $K_k$ for $G$ by removing redundant
edges between any two vertices. Based on ECT, a simple proof for four color
theorem for planar graph is then proposed.

19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph