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
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Book ChapterDOI
Graph Theoretic Techniques for Cluster Analysis Algorithms
TL;DR: The most desirable cluster analysis models for substantive applications should have the input proximity data expressible in a manner faithfully representing only the reliable information content of the empirically measured data.
Posted Content
Listing All Maximal Cliques in Large Sparse Real-World Graphs
David Eppstein,Darren Strash +1 more
TL;DR: This work implements a new algorithm for listing all maximal cliques in sparse graphs due to Eppstein, Loffler, and Strash (ISAAC 2010) and analyzes its performance on a large corpus of real-world graphs to show that this algorithm is the first to offer a practical solution to listing allmaximal clique in large sparse graphs.
Journal ArticleDOI
Large Induced Subgraphs via Triangulations and CMSO
TL;DR: It is shown that all potential maximal cliques of $G$ can be enumerated in time and implies the existence of an exact exponential algorithm of running time ${\cal O}(1.7347^n)$ for many NP-hard problems related to finding maximum induced subgraphs with different properties.
Journal ArticleDOI
The number of independent sets in unicyclic graphs
TL;DR: Upper and lower bounds for the number of independent sets in a unicyclic graph in terms of its order are determined and the extremal graphs are characterized.
Journal ArticleDOI
3-Colorability ∈ P for P 6 -free graphs
Bert Randerath,Ingo Schiermeyer +1 more
TL;DR: In this paper, it was shown that 3-colorability can be decided in polynomial time for the class of P6-free graphs with bounded dominating subgraphs.
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