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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Bounding the feedback vertex number of digraphs in terms of vertex degrees
TL;DR: It is shown how the Turan bound and the Caro-Wei inequality can be generalized to directed graphs, thus yielding a bound on directed feedback vertex number in Terms of vertex out-degrees and in terms of average out-degree, respectively.
Incremental and parallel algorithms for dense subgraph mining
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Cliques in graphs with bounded minimum degree
TL;DR: A construction is given, which is conjecture to give all extremal graph (subject to certain conditions on n, d and r), that is to say, all graphs with n vertices and minimum degree d.
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Distribution-Free Models of Social Networks
Tim Roughgarden,C. Seshadhri +1 more
TL;DR: This chapter surveys recent proposals of more robust models of large-scale social networks using generative models, a form of average-case analysis that posit deterministic and empirically supported combinatorial structure rather than a specific probability distribution.
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The growth rate over trees of any family of set defined by a monadic second order formula is semi-computable
TL;DR: It is shown that, for any monadic second order formula over graphs that characterizes a given kind of subset of its vertices, the maximal number of such sets in a tree can be expressed as the growth rate of a bilinear system.
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