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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Posted Content
Change-Sensitive Algorithms for Maintaining Maximal Cliques in a Dynamic Graph.
TL;DR: This work considers the maintenance of the set of all maximal cliques in a dynamic graph that is changing through the addition or deletion of edges, and presents nearly tight bounds on the magnitude of change, as well as the first change-sensitive algorithms for clique maintenance, whose runtime is proportional to the magnitude.
Journal ArticleDOI
The typical structure of maximal triangle-free graphs
TL;DR: In this paper, it was shown that almost every maximal triangle-free graph G admits a vertex partition X[ Y such that G[X] is a perfect matching and Y is an independent set.
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Maximal induced matchings in triangle-free graphs
TL;DR: It is proved that every n-vertex triangle-free graph has at most 3n/3≈1.4423n maximal induced matchings; this bound is attained by every disjoint union of copies of the complete bipartite graph K3, 3.5849n.
Book ChapterDOI
Some New Tractable Classes of CSPs and Their Relations with Backtracking Algorithms
TL;DR: The complexity of algorithms for solving CSPs which are classically implemented in real practical solvers, such as Forward Checking or Bactracking with Arc Consistency are investigated and a new parameter for measuring their complexity is introduced and then new complexity bounds are derived.
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