Journal ArticleDOI
On cliques in graphs
J. W. Moon,L. Moser +1 more
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TLDR
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
Maximal induced matchings in triangle-free graphs ⋆
TL;DR: It is proved that every \(n\)-vertex triangle-free graph has at most \(3^{n/3}\approx 1.4423^n\) maximal induced matchings, and this bound is attained by every disjoint union of copies of the complete bipartite graph \(K_{3,3}\).
Comparison of Clique-Listing Algorithms.
TL;DR: Five cliqueor MIS-listing algorithms are compared, and variations of the Bron and Kerbosch algorithm appear to be the fastest for random graphs and a type of graph which arises in physical mapping of genomes.
Journal Article
Merrifield-simmons index and minimum number of independent sets in short trees
TL;DR: The lower bound for the number of independent sets in a tree of fixed order and diameter d is 5 and the structure of the extremal trees is given.
Dissertation
Convex relaxation for the planted clique, biclique, and clustering problems
TL;DR: Both instances of the k-disjoint-clique problem can be formulated as rank constrained optimization problems and relaxed to semidefinite programs using the nuclear norm relaxation of rank.
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