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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Efficient Exact Algorithms through Enumerating Maximal Independent Sets and Other Techniques
TL;DR: The algorithms that are presented are the best known and are a substantial improvement over previous best results.
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Trimmed Moebius Inversion and Graphs of Bounded Degree
TL;DR: Chung et al. as discussed by the authors proposed a trimmed Moebius inversion algorithm for combinatorial optimisation problems on graphs with maximum degree Δ, and showed that for any constant Δ, these bounds are O((2−e) n ) for e>0 independent of the number of vertices.
Constructing Algorithms for Constraint Satisfaction and Related Problems : Methods and Applications
TL;DR: This thesis discusses the construction of algorithms for solving Constraint Satisfaction Problems (CSPs), and describes two new ways of approaching them, based on the idea that it is sometimes faster to solve a large number of restricted problems than a single, large, problem.
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The structure and maximum number of maximum independent sets in trees
TL;DR: The number of maximum independent sets is shown to depend on the structure within the tree of the α-critical edges and the families of trees on which these maxima are achieved are given.
Proceedings ArticleDOI
Efficient Enumeration of Maximal k-Plexes
TL;DR: This paper presents the first provably efficient algorithms, both for enumeration the maximal k-plexes and for enumerating the maximal connected k-Plexes, and their scalability with respect to graph size, density and choice of k, as well as their clear superiority over the state-of-the-art.
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