Algorithmic graph theory and perfect graphs
About: This article is published in Order.The article was published on 1986-06-01. It has received 1324 citations till now. The article focuses on the topics: Trivially perfect graph & Perfect graph theorem.
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Book•
27 Jul 2015
TL;DR: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area, providing a toolbox of algorithmic techniques.
Abstract: This comprehensive textbook presents a clean and coherent account of most fundamental tools and techniques in Parameterized Algorithms and is a self-contained guide to the area. The book covers many of the recent developments of the field, including application of important separators, branching based on linear programming, Cut & Count to obtain faster algorithms on tree decompositions, algorithms based on representative families of matroids, and use of the Strong Exponential Time Hypothesis. A number of older results are revisited and explained in a modern and didactic way. The book provides a toolbox of algorithmic techniques. Part I is an overview of basic techniques, each chapter discussing a certain algorithmic paradigm. The material covered in this part can be used for an introductory course on fixed-parameter tractability. Part II discusses more advanced and specialized algorithmic ideas, bringing the reader to the cutting edge of current research. Part III presents complexity results and lower bounds, giving negative evidence by way of W[1]-hardness, the Exponential Time Hypothesis, and kernelization lower bounds. All the results and concepts are introduced at a level accessible to graduate students and advanced undergraduate students. Every chapter is accompanied by exercises, many with hints, while the bibliographic notes point to original publications and related work.
1,544 citations
Cites background from "Algorithmic graph theory and perfec..."
...The book of Golumbic [231] discusses different algorithmic and structural properties of classes of perfect graphs, and in particular of chordal and interval graphs....
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Book•
17 Dec 1994
TL;DR: In this article, the Conjectures of Hadwiger and Hajos are used to define graph types, such as planar graph, graph on higher surfaces, and critical graph.
Abstract: Planar Graphs. Graphs on Higher Surfaces. Degrees. Critical Graphs. The Conjectures of Hadwiger and Hajos. Sparse Graphs. Perfect Graphs. Geometric and Combinatorial Graphs. Algorithms. Constructions. Edge Colorings. Orientations and Flows. Chromatic Polynomials. Hypergraphs. Infinite Chromatic Graphs. Miscellaneous Problems. Indexes.
1,380 citations
TL;DR: This survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class.
1,197 citations
Cites background from "Algorithmic graph theory and perfec..."
...A graph is a perfect elimination graph, if and only if it is a chordal graph (see [43], Chapter 4)....
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...See [43] for more information on chordal graphs and other perfect graphs....
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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
Cites background from "Algorithmic graph theory and perfec..."
...The class of perfect graphs contains many well known graphs in the literature [146], among them bipartite graphs, interval graphs, and triangulated graphs [128], [120], [288], [289], [307]....
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...Although the minimum weighted coloring problem on triangulated graphs is known to be in class P (see [146]), there was no algorithm in the literature that had reasonable time complexity....
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Book•
31 Jan 1993
TL;DR: This book is a core reference for graduate students and CAD professionals and presents a balance of theory and practice in a intuitive manner.
Abstract: From the Publisher:
This work covers all aspects of physical design. The book is a core reference for graduate students and CAD professionals. For students, concept and algorithms are presented in an intuitive manner. For CAD professionals, the material presents a balance of theory and practice. An extensive bibliography is provided which is useful for finding advanced material on a topic. At the end of each chapter, exercises are provided, which range in complexity from simple to research level.
927 citations
References
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01 Jan 1985273 citations
TL;DR: A more general paradigm for studying various classes of graphs is suggested which can be described as follows: when 9 is allowed to be an arbitrary family of sets, the class obtained as intersection graphs is all undirected graphs.
63 citations