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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Proceedings ArticleDOI
Towards automatic recommendation of friend lists
Kelli Bacon,Prasun Dewan +1 more
TL;DR: This work automates Facebook access-control lists by merging virtual friend cliques using certain heuristics that determine if two virtual friendCliques correspond to a single actual friend clique.
Journal ArticleDOI
Maximal independent sets in caterpillar graphs
Carmen Ortiz,Monica Villanueva +1 more
TL;DR: This work provides a polynomial time algorithm to generate the whole family of mis in a caterpillar graph and characterize the independent graph and the clique graph (intersection graph of cliques) of complete caterpillar graphs.
Book ChapterDOI
Sparse Square Roots
TL;DR: It is shown that it can be decided in polynomial time whether a graph of maximum degree 6 has a square root; if asquare root exists, then the algorithm finds one with minimum number of edges if it exists; and an exact exponential time algorithm is given for the problem of finding a squareRoot with maximum number of edge.
Journal ArticleDOI
Sublinear-Space and Bounded-Delay Algorithms for Maximal Clique Enumeration in Graphs
TL;DR: This paper presents efficient algorithms for listing maximal cliques in undirected graphs, providing the first sublinear-space bounds with guaranteed delay per solution.
Journal ArticleDOI
Parameterized Algorithms for Finding Square Roots
TL;DR: The first result implies that squares of graphs obtained from trees by adding at most $$k$$k edges can be recognized in polynomial time for every fixed $$k\ge 0$$k≥0; previously this result was known only for $$k=0$$ k=0.
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