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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New parameterized algorithms for edge dominating set
TL;DR: This paper shows that the parameterized edge dominating set problem can be solved in O*(2.3147^k) time and polynomial space and can be reduced to a quadratic kernel with O(k^3) edges.
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Maximum Modulus of Independence Roots of Graphs and Trees
Jason I. Brown,Ben Cameron +1 more
TL;DR: In this article, it was shown that the maximum modulus of an independence root over all trees on trees on vertices in terms of the number of independent sets of each size and their roots are defined as independence roots.
Dissertation
Computational techniques in finite semigroup theory
TL;DR: In this article, the authors present algorithms for computing maximal subsemigroups of an arbitrary finite semigroup, building on the paper of Graham, Graham, and Rhodes from 1968.
Journal ArticleDOI
Assyrian merchants meet nuclear physicists: history of the early contributions from social sciences to computer science. The case of automatic pattern detection in graphs (1950s--1970s)
TL;DR: In this paper, a socio-historical approach with an experimental reconstruction of programs is used to investigate the early automation of clique detection algorithms, which remains one of the unsolved NP-complete problems today.
Journal ArticleDOI
Homothetic polygons and beyond: Maximal cliques in intersection graphs
Valentin E. Brimkov,Konstanty Junosza-Szaniawski,Sean Kafer,Jan Kratochvíl,Martin Pergel,Paweł Rzążewski,Matthew Szczepankiewicz,Joshua Terhaar +7 more
TL;DR: It is shown that for every convex polygon P with sides parallel to k directions, every n -vertex graph which is an intersection graph of homothetic copies of P contains at most n k inclusion-wise maximal cliques.
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