Journal ArticleDOI
Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph
TLDR
This paper presents ways for constructing efficient algorithms for finding a minimum coloring, a minimum covering by cliques, a maximum clique, and a maximum independent set given a chordal graph.Abstract:
A finite undirected graph is called chordal if every simple circuit has a chord. Given a chordal graph, we present, ways for constructing efficient algorithms for finding a minimum coloring, a minimum covering by cliques, a maximum clique, and a maximum independent set. The proofs are based on a theorem of D. Rose [3] that a finite graph is chordal if and only if it has some special orientation called an R-orientation. In the last part of this paper we prove that an infinite graph is chordal if and only if it has an R-orientation.read more
Citations
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Local computations with probabilities on graphical structures and their application to expert systems
Book
Introduction to Algorithms, Second Edition
TL;DR: The complexity class P is formally defined as the set of concrete decision problems that are polynomial-time solvable, and encodings are used to map abstract problems to concrete problems.
Journal ArticleDOI
Some simplified NP-complete graph problems
TL;DR: This paper shows that a number of NP - complete problems remain NP -complete even when their domains are substantially restricted, and determines essentially the lowest possible upper bounds on node degree for which the problems remainNP -complete.
Journal ArticleDOI
Algorithmic Aspects of Vertex Elimination on Graphs
TL;DR: A graph-theoretic elimination process which is related to performing Gaussian elimination on sparse symmetric positive definite systems of linear equations is considered, and it is conjecture that the problem of finding a minimum ordering is NP-complete.
Journal ArticleDOI
Frequency assignment: Theory and applications
TL;DR: This paper introduces the minimum-order approach to frequency assignment and presents a theory which relates this approach to the traditional one, and shows that many frequency assignment problems are equivalent to generalized graph coloring problems.
References
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Incidence matrices and interval graphs
TL;DR: In this article, the problem of determining when a graph is an interval graph is a special case of the following problem concerning (0, 1)-matrices: when can the rows of such a matrix be permuted so as to make the 1's in each colum appear consecutively.
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Introduction to mathematical logic
Hans Hermes,Diana Schmidt +1 more
TL;DR: This book discusses the semantics of Predicate Logic, and some of theorems of A. Robinson, Craig and Beth's treatment of Peano's Axiom System.
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Triangulated graphs and the elimination process
TL;DR: In this paper, a triangulated graph is defined as a graph in which for every cycle of length l > 3, there is an edge joining two nonconsecutive vertices.
Journal ArticleDOI
Permutation Graphs and Transitive Graphs
TL;DR: Algorithms for finding a maximum size clique and a minimum coloration of transitive grapl are presented and are applicable in solving problems in memo] allocation and circuit layout.