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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Journal ArticleDOI
Applications of graph theory in protein structure identification.
TL;DR: A review of graph-theoretic methods for protein structure identification can be found in this article, where the authors mainly introduce classical methods and mathematical models including homology modeling based on clique finding, identification of side-chain clusters in protein structures upon graph spectrum, and de novo peptide sequencing via tandem mass spectrometry using the spectrum graph model.
Posted Content
Finding Cliques in Social Networks: A New Distribution-Free Model
TL;DR: In this article, the authors proposed a new distribution-free model of social networks, called "weakly $c$-closed" graphs, where for every pair of vertices $u,v$ with at least common neighbors, $u$ and $v$ are adjacent.
Journal ArticleDOI
Counting Maximal Antichains and Independent Sets
Liviu Ilinca,Jeff Kahn +1 more
TL;DR: Answering several questions of Duffus, Frankl and Rödl, asymptotics for the logarithms of (i) the number of maximal antichains in the n-dimensional Boolean algebra and (ii) the numbers of maximal independent sets in the covering graph of then-dimensional hypercube and certain natural subgraphs thereof are given.
Proceedings ArticleDOI
Economic-robust transmission opportunity auction in multi-hop wireless networks
TL;DR: This paper proposes a transmission opportunity auction scheme, called TOA, which can support multi-hop data traffic, ensure economic-robustness, and generate high revenue for the auctioneer, and proves that TOA is economic-Robust.
Journal ArticleDOI
All maximal independent sets and dynamic dominance for sparse graphs
TL;DR: In this article, the authors describe algorithms based on Avis and Fukuda's reverse search paradigm for enumerating maximal independent sets in a sparse graph in polynomial time and delay per output.
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