Maximum internally stable sets of a graph
S.L Hakimi,H Frank +1 more
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This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1969-02-01 and is currently open access. It has received 10 citations till now. The article focuses on the topics: Graph (abstract data type).read more
Citations
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Book ChapterDOI
The maximum clique problem
TL;DR: A survey of results concerning algorithms, complexity, and applications of the maximum clique problem is presented and enumerative and exact algorithms, heuristics, and a variety of other proposed methods are discussed.
Journal ArticleDOI
Steiner's problem in graphs and its implications
TL;DR: A graph theoretic version of Steiner's problem in plane geometry is described and it is shown that a solution to this problem provides us with a solutions to the problems of finding a minimum externally stable set and a maximum internally stable set in a graph.
Journal ArticleDOI
Graph theoretic error-correcting codes
S. Hakimi,J. Bredeson +1 more
TL;DR: A study of the efficiency, error-correcting capabilities, and limitations of graph theoretic block codes is presented and it is shown that such augmentation techniques can substantially increase the level of efficiency of these codes and potentially could increase it to thelevel of the best available codes.
Journal ArticleDOI
Clique detection for nondirected graphs: Two new algorithms
L. Gerhards,W. Lindenberg +1 more
TL;DR: Two new methods for determining all maximal complete subgraphs (cliques) of a finite nondirected graph are described, in both methods the blockwise generation of all cliques induces characteristic properties, which guarantee an efficient calculation of special clique subsets.
Journal ArticleDOI
A depth first search algorithm to generate the family of maximal independent sets of a graph lexicographically
TL;DR: A depth first search algorithm to generate the family of maximal independent sets of an undirected graph lexicographically is presented, which is at least three times faster than the Bron and Kerbosch algorithm and becomes increasingly more efficient as both the density and size of the graph increase.
References
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Book ChapterDOI
Paths, Trees, and Flowers
TL;DR: A graph G is a set of elements called vertices and a finite set of edges called edges such that each edge meets exactly two vertices, called the end-points of the edge as mentioned in this paper.
Book
Theory of graphs
TL;DR: In this article, the axiom of choice of choice is used to define connectedness path problems in directed graphs and cyclic graphs, as well as Galois correspondences of connectedness paths.
Journal ArticleDOI
An algorithm for a minimum cover of a graph
TL;DR: In this paper, the problem of finding a simple algorithm for finding a minimum cover of a graph was proposed as the one-dimensional instance of the more general question of finding the minimum cover for a cubical complex.
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