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
On the Maximum Number of Cliques in a Graph
TL;DR: The maximum number of cliques in a graph for the following graph classes is determined: graphs with n vertices and m edges, d-degenerate graphs, and planar graphs.
Book ChapterDOI
Small Maximal Independent Sets and Faster Exact Graph Coloring
TL;DR: In this article, it was shown that for any n-vertex graph G and integer parameter k, there are at most 34k-n4n-3k maximal independent sets I ⊂ G with |I| ≤ k, and that all such sets can be listed in time O(34k n4n3k).
Journal ArticleDOI
Enumeration aspects of maximal cliques and bicliques
TL;DR: The notion of the transition graph T(G) whose vertices are maximal cliques of G and arcs are transitions between cliques is introduced and it is shown that under some specific numbering, the transition graphs has a hamiltonian path for chordal and comparability graphs.
Journal ArticleDOI
Capacity-Aware and Delay-Guaranteed Resilient Controller Placement for Software-Defined WANs
TL;DR: This paper proposes a solution for a resilient controller placement problem that takes both the switch-controller /inter-controller latency requirements and the capacity of the controllers into account to meet the traffic load of switches.
Proceedings ArticleDOI
Randomized graph products, chromatic numbers, and Lovasz j-function
TL;DR: It is proved that for somec>0, there exists an infinite family of graphs such that vartheta (G) > α (G), where n denotes the number of vertices in a graph and this disproves a known conjecture regarding the ϑ function.
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