Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Maximum Number of 3- and 4-Cliques within a Planar Maximally
  Filtered Graph   Planar Maximally Filtered Graphs (PMFG) are an important tool for filtering
the most relevant information from correlation based networks such as stock
market networks. One of the main characteristics of a PMFG is the number of its
3- and 4-cliques. Recently in a few high impact papers it was stated that,
based on heuristic evidence, the maximum number of 3- and 4-cliques that can
exist in a PMFG with n vertices is 3n - 8 and n - 4 respectively. In this
paper, we prove that this is indeed the case.

5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an