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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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On Common Intervals with Errors
TL;DR: This work contributes a model defining gene clusters as common intervals with errors and discusses different representations and the corresponding problems resulting for the search procedure.
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On the number of minimal transversals in 3-uniform hypergraphs
TL;DR: It is proved that the number of minimal transversals in a 3-uniform hypergraph with n vertices is at most c^n, where c~1.6702 is a constant.
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Trees with the second largest number of maximal independent sets
Min-Jen Jou,Jenq-Jong Lin +1 more
TL;DR: In this article, the second largest number of maximal independent sets among all trees and forests of order n>=4 was determined, and the extremal graphs achieving these values were characterized.
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Constraints on the number of maximal independent sets in graphs
TL;DR: This work proves two conjectures, suggested by P. Erdos, that the maximum number of maximal independent sets among all graphs of order n in a family Φ is o(3n/3) ifΦ is either a family of connected graphs such that the largest value of maximum degrees among all graph n in Φ are o(n) or a family that approaches infinity as n → ∞.
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