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
From Tree Path-Factors and Doubly Exponential Sequences to a Binomial Inequality
TL;DR: In this paper, the authors report on a research that led to the formulation of the following constrained inequality between products of some binomial coefficients, which they call the constrained inequality of the product of the products of the binomial coefficient.
Reference EntryDOI
Maximum Clique, Maximum Independent Set, and Graph Coloring Problems
Jeffrey Pattillo,Sergiy Butenko +1 more
TL;DR: In this paper, the authors introduce the closely related maximum clique, maximum independent set, graph coloring, and minimum clique partitioning problems, including their computational complexity, known bounds, mathematical programming formulations, and exact and heuristic algorithms.
Journal ArticleDOI
An algorithm for obtaining the chromatic number and an optimal coloring of a graph
S. I. Roschke,Antonio L. Furtado +1 more
Journal ArticleDOI
On maximum independent set of categorical product and ultimate categorical ratios of graphs
TL;DR: It is proved that computing the maximum independent set of the categorical product of a planar graph of maximum degree three and a K 4 is NP-complete and the ultimate categorical independence ratio of general graphs is zero.
Proceedings ArticleDOI
Attribute Compartmentation and Greedy UCC Discovery for High-Dimensional Data Anonymization
TL;DR: It is shown that by identifying dependencies between attribute subsets the authors can eliminate privacy violating attributes from the anonymised dataset and employ a greedy search algorithm to determine and eliminate maximal partial unique attribute combinations.
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