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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Journal ArticleDOI
An algorithm for finding all maximal complete subgraphs and an estimate of the order of computational complexity
Sunil R. Das,C.L. Sheng,Zen Chen +2 more
TL;DR: In this article, the authors propose an algorithm for finding all maximal complete subgraphs or cliques of an undirected graph. But their algorithm is based on a refinement of the technique of successive splitting described by Paull and Unger in the determination of maximal compatibles of states in the context of minimization of incomplete sequential machines.
Posted Content
Maximal and Maximum Dissociation Sets in General and Triangle-Free Graphs
Jianhua Tu,Yuxin Li,Junfeng Du +2 more
TL;DR: The upper bound on the number of maximal dissociation sets in general and in triangle-free graphs was shown in this paper, where it was shown that every graph of order n has at most (1 − ε)-minimal dissociation set of maximum degree at most 1.
Book ChapterDOI
An Enhanced Infra-Chromatic Bound for the Maximum Clique Problem
TL;DR: A way to enhance exact solvers with an additional infra-chromatic bounding function is described and performance over a number of graphs from well known data sets is reported.
DissertationDOI
Topological structure of spatially-distributed network coded information
TL;DR: This paper defines the coverage complex, a new type of simplicial complex built on the nodes of the network which captures properties of the data coverage, and uses tools from algebraic topology, persistent homology, and matroid theory to study it.
Book ChapterDOI
Open Problems in Abstract Argumentation
Ringo Baumann,Hannes Strass +1 more
TL;DR: In this paper, the authors give a list of currently unsolved problems in abstract argumentation, and motivate why it is interesting and what makes it apparently hard to solve, for each of the problems.
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