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
Complexity aspects of the Helly property: graphs and hypergraphs.
TL;DR: In this paper, the authors survey complexity aspects of the Helly property, and describe algorithms for solving different problems arising from the basic Helly properties, some of them leading to NP-hardness results.
Journal ArticleDOI
Maximal independent sets in bipartite graphs
TL;DR: The maximum number of maximal independent sets among all bipartite graphs of order n and the extremal graphs as well as the corresponding results for connected bipartites graphs are determined.
Book ChapterDOI
On Independent Sets and Bicliques in Graphs
TL;DR: It is shown that the maximum number of maximal bicliques in a graph on n vertices is exactly 3 n /3 (up to a polynomial factor).
Journal ArticleDOI
The number of maximal sum-free subsets of integers
TL;DR: In this paper, it was shown that there are at most 2 (1=4+o(1))n maximal sum-free sets in f1;:::;ng.
Journal ArticleDOI
Coalition logic with individual, distributed and common knowledge
Thomas Ågotnes,Natasha Alechina +1 more
TL;DR: This paper proves completeness for epistemic coalition logic with common knowledge, with distributedknowledge, and with both common and distributed knowledge, respectively, and completely characterise the complexity of the satisfiability problem for each of the three logics.
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