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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Fundamental Study Enumerating all connected maximal common subgraphs in two graphs
TL;DR: A new method for finding all connected maximal common subgraphs in two graphs which is based on the transformation of the problem into the clique problem and the runtimes for all variants by means of random graphs are discussed.
Journal ArticleDOI
Enumerating all connected maximal common subgraphs in two graphs
TL;DR: In this paper, a new method for finding all connected maximal common subgraphs in two graphs is presented based on the transformation of the problem into the clique problem, which is based on variants of the Bron-Kerbosch algorithm.
Journal ArticleDOI
Technical Section: Fast construction of the Vietoris-Rips complex
TL;DR: This work formulate a two-phase approach for the Vietoris-Rips complex that separates geometry from topology, and gives three algorithms for the second phase, and implements all algorithms.
Journal ArticleDOI
Clique-detection models in computational biochemistry and genomics
TL;DR: The proposed article includes an introduction to the underlying biochemistry and genomic aspects of the problems as well as to the graph-theoretic aspects ofThe solution approaches, which describes a particular type of problem, and gives an example to show how the graph model can be derived.
Journal ArticleDOI
A graph-theoretic algorithm for comparative modeling of protein structure
TL;DR: An algorithm that uses graph theory to handle the interconnected nature of interactions in protein structures and is used in a comparative modeling scenario to build side-chains, regions of main chain, and mix and match between different homologs in a context-sensitive manner.
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