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
Minimum vertex blocker clique problem
TL;DR: The first exact algorithm for solving VBCP is developed, which solves the proposed formulation by using a row generation approach, and an analytical lower bound on the cardinality of an optimal solution to V BCP is presented.
Proceedings ArticleDOI
Efficient cohesive subgraphs detection in parallel
Yingxia Shao,Lei Chen,Bin Cui +2 more
TL;DR: A novel parallel and efficient truss detection algorithm, called PeTa, which produces a triangle complete subgraph (TC-subgraph) for every computing node and can detect the local k-truss in parallel within a few iterations.
Journal ArticleDOI
Fast algorithms for min independent dominating set
TL;DR: Approximation of the problem by moderately exponential time algorithms is studied and it is shown that it can be approximated within ratio [email protected], for any @e>0, in a time smaller than the one of exact computation and exponentially decreasing with @e.
Dissertation
Average-case complexity of detecting cliques
Madhu Sudan,Benjamin Rossman +1 more
TL;DR: The results show that, in certain models of computation, solving k-CLIQUE in the average case requires Ω( nk/4) resources (moreover, k/4 is tight), and obtain a novel Size Hierarchy Theorem for uniform AC0.
Journal ArticleDOI
The number of maximum independent sets in graphs
Min-Jen Jou,Gerard J. Chang +1 more
TL;DR: In this article, the problem of determining the largest number of maximum independent sets of a graph of order n is studied, and solutions to this problem are given for various classes of graphs, including general graphs, trees, forests, (connected) graphs with at most one cycle, connected graphs and triangle-free graphs.
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