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Journal ArticleDOI

On cliques in graphs

J. W. Moon, +1 more
- 01 Mar 1965 - 
- Vol. 3, Iss: 1, pp 23-28
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TLDR
In this article, the maximum number of cliques possible in a graph with n nodes is determined and bounds are obtained for the number of different sizes of clique possible in such a graph.
Abstract
A clique is a maximal complete subgraph of a graph. The maximum number of cliques possible in a graph withn nodes is determined. Also, bounds are obtained for the number of different sizes of cliques possible in such a graph.

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Book ChapterDOI

Complexity of Grundy Coloring and Its Variants

TL;DR: This paper shows that Grundy Coloring can be solved in time, and proves that under the Exponential Time Hypothesis, it cannot be computed in time \(O^*(c^{w})\), for any constant c.
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Tight lower bounds for the complexity of multicoloring

TL;DR: In this paper, the complexity of determining whether a graph has a kneser-coloring was shown to be Ω(n+1) √ poly(n) unless the exponential time hypothesis (ETH) fails.
Proceedings ArticleDOI

Detecting Highly Overlapping Community Structure by Model-based Maximal Clique Expansion

TL;DR: This work makes an original use of a particular concept of graph theory, called chordal graph, to discover densely connected structures in social interactions based on maximal cliques to propose an efficient overlapping community detection method using a seed set expansion approach.
References
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Journal ArticleDOI

On the theory of graphs

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