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
Citations
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Extremal problems related to Betti numbers of flag complexes
TL;DR: An upper bound of 1.3 2 n is proved for the sum of Betti numbers of any n -vertex flag complex and 1.2 5 n for the independence complex of a triangle-free graph, implying upper bounds for the BettiNumbers of various related classes of spaces, including the neighbourhood complex of the graph.
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Independent sets in graphs
TL;DR: A survey of enumeration of independent sets in graphs and related problems is given in this article, where the authors give a survey of the enumeration and enumeration problems in graphs.
Journal ArticleDOI
Posets with maximal Mo¨bius function
TL;DR: The absolute value of the Mobius function of a bounded poset P with n + 2 elements satisfies This bound is sharp and the posets achieving it are classified.
Journal ArticleDOI
A memetic algorithm for minimum independent dominating set problem
TL;DR: A tabu search-based memetic algorithm is designed for MIDS based on two novel ideas, i.e., the forgetting-based vertex weighting strategy and the repairing-based crossover strategy, which performs better than a previous state-of-the-art heuristic algorithm forMIDS on DIMACS benchmark.
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A two-level graph partitioning problem arising in mobile wireless communications
TL;DR: It is shown that an exact algorithm based on intelligent preprocessing, cutting planes and symmetry-breaking is capable of solving small- and medium-size instances to proven optimality, and providing strong lower bounds for larger instances.
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