Topic
Chordal graph
About: Chordal graph is a research topic. Over the lifetime, 12858 publications have been published within this topic receiving 314218 citations.
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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.
Abstract: The maximum clique problem is a classical problem in combinatorial optimization which finds important applications in different domains. In this paper we try to give a survey of results concerning algorithms, complexity, and applications of this problem, and also provide an updated bibliography. Of course, we build upon precursory works with similar goals [39, 232, 266].
1,065 citations
TL;DR: An article of golfing equipment has a golf tee attached to a spring-biassed reel by a length of string which can be aligned with the green or hole and used as an aid in swinging the club face in the correct direction.
Abstract: Chordal graphs arise naturally in the study of Gaussian elimination on sparse symmetric matrices; acyclic hypergraphs arise in the study of relational data bases. Rose, Tarjan and Lueker [SIAM J. C...
991 citations
01 May 2000
TL;DR: A random graph model is proposed which is a special case of sparse random graphs with given degree sequences which involves only a small number of parameters, called logsize and log-log growth rate, which capture some universal characteristics of massive graphs.
Abstract: We propose a random graph model which is a special case of sparse random graphs with given degree sequences. This model involves only a small number of parameters, called logsize and log-log growth rate. These parameters capture some universal characteristics of massive graphs. Furthermore, from these parameters, various properties of the graph can be derived. For example, for certain ranges of the parameters, we will compute the expected distribution of the sizes of the connected components which almost surely occur with high probability. We will illustrate the consistency of our model with the behavior of some massive graphs derived from data in telecommunications. We will also discuss the threshold function, the giant component, and the evolution of random graphs in this model.
979 citations
01 Jan 2003
TL;DR: As most ‘real-world’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data, but only very specific graphs such as trees and strings have been considered.
Abstract: As most ‘real-world’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data. One of the most widely used tools for modeling structured data are graphs. An interesting and important challenge is thus to investigate kernels on instances that are represented by graphs. So far, only very specific graphs such as trees and strings have been considered.
960 citations
TL;DR: Using a variation of the interpretability concept, it is shown that all graph properties definable in monadic second-order logic with quantification over vertex and edge sets can be decided in linear time for classes of graphs of fixed bounded treewidth given a tree-decomposition.
940 citations