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
A scalable, parallel algorithm for maximal clique enumeration
TL;DR: This paper proposes a parallel, scalable, and memory-efficient MCE algorithm for distributed and/or shared memory high performance computing architectures, whose runtime scales linearly for thousands of processors on real-world application graphs with hundreds and thousands of nodes.
Journal ArticleDOI
Vertex Colouring and Forbidden Subgraphs – A Survey
Bert Randerath,Ingo Schiermeyer +1 more
TL;DR: This work surveys results on vertex colourings of graphs defined in terms of forbidden induced subgraph conditions in order to obtain useful results from a graph coloring formulation of his problem.
Proceedings ArticleDOI
Detectives: detecting coalition hit inflation attacks in advertising networks streams
TL;DR: This paper describes the advertising network model, and focuses on the most sophisticated type of fraud, which involves coalitions among fraudsters, and builds on several published theoretical results to devise the Similarity-Seeker algorithm that discovers coalitions made by pairs of fraudsters.
Journal ArticleDOI
Enumerating maximal independent sets with applications to graph colouring
TL;DR: Improved algorithms for graph colouring and computing the chromatic number of a graph are constructed by giving tight upper bounds on the number of maximal independent sets of size k in graphs with n vertices.
Journal ArticleDOI
On graphs with polynomially solvable maximum‐weight clique problem
Egon Balas,Chang-Sung Yu +1 more
TL;DR: A family of graphs with polynomially solvable maximum weight clique problem is identified using the edge-bicoloring approach developed in a a recent paper by Balas, Chvatal and Nesetril.
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