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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Journal ArticleDOI
Clique detection for nondirected graphs: Two new algorithms
L. Gerhards,W. Lindenberg +1 more
TL;DR: Two new methods for determining all maximal complete subgraphs (cliques) of a finite nondirected graph are described, in both methods the blockwise generation of all cliques induces characteristic properties, which guarantee an efficient calculation of special clique subsets.
Book ChapterDOI
Efficient Algorithms for Finding Maximum and Maximal Cliques: Effective Tools for Bioinformatics
TL;DR: This chapter presents efficient algorithms for finding a maximum clique and maximal cliques as effective tools for bioinformatics, and shows the successful applications of these algorithms to bio informatics.
Journal ArticleDOI
Graph with given achromatic number
Pavol Hell,Donald J. Miller +1 more
TL;DR: It is proved that there are only finitely many irreducible graphs with a given achromatic number, and all graph with a chromatic number less than four are described.
Proceedings ArticleDOI
3-coloring in time 0(1.3446/sup n/): a no-MIS algorithm
Richard Beigel,David Eppstein +1 more
TL;DR: This work gives a fast algorithm for (3,2)-SSS and uses it to improve the time bounds for solving the other problems listed above.
Journal ArticleDOI
A depth first search algorithm to generate the family of maximal independent sets of a graph lexicographically
TL;DR: A depth first search algorithm to generate the family of maximal independent sets of an undirected graph lexicographically is presented, which is at least three times faster than the Bron and Kerbosch algorithm and becomes increasingly more efficient as both the density and size of the graph increase.
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