Journal ArticleDOI
On cliques in graphs
J. W. Moon,L. Moser +1 more
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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.read more
Citations
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Proceedings ArticleDOI
Finding a Summary for All Maximal Cliques
TL;DR: In this article, the authors propose to restrict the bound calculation operation to a particular subset of all search branches and make the best use of the bounds that have been previously calculated to speed up the process of finding a maximal clique summary.
Journal ArticleDOI
S-bite
TL;DR: S-BITE is the first generator that successfully targets the problem of both matching classical graph metrics, such as the degree distribution, and representing the Internets structure, in the form of maximal cliques, which leads to a huge reduction in complexity and shows that the core of the large-scale Internet is not that large, and can be broken down into a two-layer graph.
Journal ArticleDOI
From Independent Sets and Vertex Colorings to Isotropic Spaces and Isotropic Decompositions: Another Bridge between Graphs and Alternating Matrix Spaces
TL;DR: In this article, Lovasz built a bridge between graphs and alternating matrix spaces, in the context of perfect matchings, and a similar connection between bipartititit...
Journal ArticleDOI
Groups with few maximal sum-free sets
Hong Liu,Maryam Sharifzadeh +1 more
TL;DR: It is shown that, in contrast to the integers setting, almost all even order abelian groups $G$ have exponentially fewer maximal sum-free sets than $2^{\mu (G)/2}$, where $\mu(G)$ denotes the size of a largest sum- free set in $G$.
Journal ArticleDOI
Assyrian merchants meet nuclear physicists: history of the early contributions from social sciences to computer science. The case of automatic pattern detection in graphs (1950s-1970s)
TL;DR: In this paper, a socio-historical approach with an experimental reconstruction of programs is used to investigate the early automation of clique detection algorithms, which remains one of the unsolved NP-complete problems in network analysis.
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