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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Book ChapterDOI
Exact algorithms for exact satisfiability and number of perfect matchings
Andreas Björklund,Thore Husfeldt +1 more
TL;DR: In this paper, exact algorithms with exponential running times for variants of n-element set cover problems, based on divide-and-conquer and on inclusion-exclusion characterisations, were presented.
Posted ContentDOI
Enumerating common molecular substructures
TL;DR: The problem of enumerating all maximal k-common molecular fragments of a pair of molecular graphs is introduced, and the MCCIS enumeration algorithm is extended and algorithm engineering techniques are applied to solve practical instances fast for the general k > 0 case.
Journal ArticleDOI
On the maximum number of maximum independent sets in connected graphs
Elena Mohr,Dieter Rautenbach +1 more
TL;DR: In this paper, the authors characterize the connected graphs of given order n and given independence number α that maximize the number of maximum independent sets of a given graph. But they do not characterize the graphs that arise from the disjoint union of cliques of orders n and α.
Posted Content
Implementation of exponential and parametrized algorithms in the AGAPE project
TL;DR: This technical report describes the implementation of exact and parametrized exponential algorithms, developed during the French ANR Agape during 2010-2012, written in Java using the Jung graph library.
Journal ArticleDOI
On the number of 2-packings in a connected graph
TL;DR: New asymptotic upper and lower bounds on the maximum number of 2-packings in a connected graph on n vertices are found.
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