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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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Dissertation

An Order Theoretic Point-of-view on Subgroup Discovery

TL;DR: This thesis extends the state-of-the-art by providing a unified view of the hypotheses space behind subgroup discovery using the well-founded mathematical tool of order theory, and proposing the new hypothesis space of conjunction of linear inequalities in numerical databases and the algorithms enumerating its elements.
Journal ArticleDOI

Efficient enumeration of maximal induced bicliques

TL;DR: This work proves new bounds on the maximum number of maximal induced bicliques of graphs with respect to their maximum degree Δ and degeneracy k, and provides output sensitive algorithms for this problem with enumeration time depending only on themaximum degree of the input graph.
Journal ArticleDOI

Theoretical underpinnings for maximal clique enumeration on perturbed graphs

TL;DR: By enumerating only the difference set between the baseline and perturbed graphs' MCEs, the computational cost of enumerating the maximal cliques of the perturbed graph can be reduced.
Journal ArticleDOI

A Tutorial on Clique Problems in Communications and Signal Processing

TL;DR: In this article, the structural properties of integer programs that can be formulated as clique problems through multiple examples in communications and signal processing are discussed. And the use of the clique formulation through numerous contemporary examples, mainly in maximum access for nonorthogonal multiple access networks, throughput maximization using index and instantly decodable network coding, collision-free radio-frequency identification networks, and resource allocation in cloud-radio access networks.
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Efficient Conversion of RNA Pseudoknots to Knot-Free Structures Using a Graphical Model

TL;DR: The pseudoknot removal problem was transformed into a circle graph maximum weight independent set (MWIS) problem, in which each MWIS represents a unique optimal deknotted structure and an existing circle graph MWIS algorithm was extended to report either single or all solutions.
References
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Journal ArticleDOI

On the theory of graphs

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