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
A group level validation of the supercombinatorality property: Finding high-quality ingredient combinations using pairwise information
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Proceedings ArticleDOI
Maximal clique enumeration for large graphs on hadoop framework
TL;DR: An implementation of pbitMCE using mapreduce that takes a large graph and an ordering of vertices as input and enumerates all the maximal cliques is presented and shows that the degree ordering performs comparable to the degeneracy ordering in most cases while it performs poorer in the case of large graphs.
Journal ArticleDOI
Colorings with few Colors: Counting, Enumeration and Combinatorial Bounds
TL;DR: This paper studies enumeration and counting problems on edge colorings, total colorings and L(2,1)-labelings of graphs, and dynamic programming algorithms solving counting problems.
Journal ArticleDOI
Ultrametricity indices for the Euclidean and Boolean hypercubes
TL;DR: In this article, it was shown that the three ultrametricity indices converge in probability to one as dimension increases, if the sample size remains fixed, and this holds true for random categorial data in complete disjunctive form.
Journal ArticleDOI
Computing stable models: worst-case performance estimates
TL;DR: In this paper, the authors study algorithms for computing stable models of logic programs and derive estimates on their worst-case performance that are asymptotically better than the trivial bound of O(m 2^n) where m is the size of an input program and n is the number of its atoms.
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