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The Maximum Number of 3- and 4-Cliques within a Planar Maximally Filtered Graph
July 10, 2015 Β· Declared Dead Β· π arXiv.org
"No code URL or promise found in abstract"
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Authors
Jenna Birch, Athanasios A. Pantelous, Konstantin Zuev
arXiv ID
1507.02929
Category
math-ph
Cross-listed
cs.DS
Citations
10
Venue
arXiv.org
Last Checked
3 months ago
Abstract
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.
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