Classes Of Directed Graphs
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Classes Of Directed Graphs
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Author : Jørgen Bang-Jensen
language : en
Publisher: Springer
Release Date : 2018-06-18
Classes Of Directed Graphs written by Jørgen Bang-Jensen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-18 with Mathematics categories.
This edited volume offers a detailed account of the theory of directed graphs from the perspective of important classes of digraphs, with each chapter written by experts on the topic. Outlining fundamental discoveries and new results obtained over recent years, this book provides a comprehensive overview of the latest research in the field. It covers core new results on each of the classes discussed, including chapters on tournaments, planar digraphs, acyclic digraphs, Euler digraphs, graph products, directed width parameters, and algorithms. Detailed indices ease navigation while more than 120 open problems and conjectures ensure that readers are immersed in all aspects of the field. Classes of Directed Graphs provides a valuable reference for graduate students and researchers in computer science, mathematics and operations research. As digraphs are an important modelling tool in other areas of research, this book will also be a useful resource to researchers working in bioinformatics, chemoinformatics, sociology, physics, medicine, etc.
The Classification Of Countable Homogeneous Directed Graphs And Countable Homogeneous N Tournaments
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Author : Gregory L. Cherlin
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
The Classification Of Countable Homogeneous Directed Graphs And Countable Homogeneous N Tournaments written by Gregory L. Cherlin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In this book, Ramsey theoretic methods introduced by Lachlan are applied to classify the countable homogeneous directed graphs. This is an uncountable collection, and this book presents the first explicit classification result covering an uncountable family. The author's aim is to demonstrate the potential of Lachlan's method for systematic use.
Graph Classes
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Author : Andreas Brandstadt
language : en
Publisher: SIAM
Release Date : 1999-01-01
Graph Classes written by Andreas Brandstadt and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.
This well-organized reference is a definitive encyclopedia for the literature on graph classes. It contains a survey of more than 200 classes of graphs, organized by types of properties used to define and characterize the classes, citing key theorems and literature references for each. The authors state results without proof, providing readers with easy access to far more key theorems than are commonly found in other mathematical texts. Interconnections between graph classes are also provided to make the book useful to a variety of readers.
Classification Of Countable Homogeneous Directed Graphs And Countable Homogeneous N Tournamenst
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Author : Gregory L. Cherlin
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-09-11
Classification Of Countable Homogeneous Directed Graphs And Countable Homogeneous N Tournamenst written by Gregory L. Cherlin and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with MATHEMATICS categories.
In this book, Ramsey theoretic methods introduced by Lachlan are applied to classify the countable homogeneous directed graphs. This is an uncountable collection, and this book presents the first explicit classification result covering an uncountable family. The author's aim is to demonstrate the potential of Lachlan's method for systematic use.
Digraphs
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Author : Jorgen Bang-Jensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Digraphs written by Jorgen Bang-Jensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The study of directed graphs (digraphs) has developed enormously over recent decades, yet the results are rather scattered across the journal literature. This is the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, the authors discuss a large number of applications and their generalizations to topics such as the traveling salesman problem, project scheduling, genetics, network connectivity, and sparse matrices. Numerous exercises are included. For all graduate students, researchers and professionals interested in graph theory and its applications, this book will be essential reading.
Dualities In Graphs And Digraphs
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Author : Hatzel, Meike
language : en
Publisher: Universitätsverlag der TU Berlin
Release Date : 2023-05-23
Dualities In Graphs And Digraphs written by Hatzel, Meike and has been published by Universitätsverlag der TU Berlin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-23 with Computers categories.
In this thesis we describe dualities in directed as well as undirected graphs based on tools such as width-parameters, obstructions and substructures. We mainly focus on directed graphs and their structure. In the context of a long open conjecture that bounds the monotonicity costs of a version of the directed cops and robber game, we introduce new width-measures based on directed separations that are closely related to DAG-width. We identify a tangle-like obstruction for which we prove a duality theorem. Johnson, Reed, Robertson, Seymour and Thomas introduced the width measure directed treewidth as a generalisation of treewidth for directed graphs. We introduce a new width measure, the cyclewidth, which is parametrically equivalent to directed treewidth. Making use of the connection between directed graphs and bipartite graphs with perfect matchings we characterise the digraphs of low cyclewidth. Generalising the seminal work by Robertson and Seymour resulting in a global structure theorem for undirected graphs, there is the goal of obtaining a structure theorem, based on directed treewidth, describing the structure of the directed graphs excluding a fixed butterfly minor. Working in this direction we present a new flat wall theorem for directed graphs which we believe to provide a better base for a directed structure theorem than the existing ones. On undirected graphs we present several results on induced subgraphs in the graphs themselves or the square graph of their linegraph. These results range from general statements about all graphs to the consideration of specific graph classes such as the one with exactly two moplexes. In der vorliegenden Arbeit beschreiben wir Dualitäten in gerichteten sowie in ungerichteten Graphen basierend auf Konzepten wie Weiteparametern, Obstruktionen und Substrukturen. Der Hauptfokus der Arbeit liegt bei gerichteten Graphen und ihrer Struktur. Im Kontext einer lange offenen Vermutung, dass die Monotoniekosten einer Variante des Räuber und Gendarm Spiels für gerichtete Graphen beschränkt sind, führen wir neue Weiteparameter ein, die auf gerichteten Separationen basieren und eng mit DAG-Weite verwandt sind. Wir identifizieren Tangle-artige Obstruktionen zu diesen Weiteparametern und beweisen die Dualität zwischen diesen beiden Konzepten. Johnson, Reed, Robertson, Seymour und Thomas haben die gerichtete Baumweite als gerichtete Verallgemeinerung der Baumweite auf ungerichteten Graphen eingeführt. Wir führen einen neuen Weiteparameter, die Cyclewidth, ein, der parametrisch equivalent zur gerichteten Baumweite ist. Unter Nutzung der Verwandtschaft von gerichteten Graphen und bipartiten Graphen mit perfekten Matchings charakterisieren wir die gerichteten Graphen mit kleiner Cyclewidth. Ein einschlagendes Ergebnis in der Graphenstrukturtheorie ist das Strukturtheorem von Robertson und Seymour. Basierend darauf gibt es Anstrengungen ein solches Strukturtheorem auch für gerichtete Graphen zu finden und dafür die gerichtete Baumweite als Grundlage zu nutzen. Dieses Theorem soll die Struktur aller gerichteten Graphen beschreiben, die einen festen gerichteten Graphen als Butterflyminoren ausschließen. In diesem Kontext beweisen wir ein neues Flat-wall-theorem für gerichtete Graphen, dass unserer Erwartung nach eine bessere Basis für ein gerichtetes Strukturtheorem bietet als die bisher betrachteten Alternativen. Auf ungerichteten Graphen präsentieren wir einige Ergebnisse bezüglich induzierten Subgraphen in gegebenen Graphen oder ihren Linegraphen. Diese Ergebnisse reichen von der Betrachtung spezifischer Graphklassen, wie den Graphen mit zwei Moplexen, bis zu Ergebnissen auf der allgemeinen Klasse aller Graphen.
Sparsity
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Author : Jaroslav Nešetřil
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-24
Sparsity written by Jaroslav Nešetřil and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-24 with Mathematics categories.
This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetřil is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010.
Quantitative Graph Theory
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Author : Matthias Dehmer
language : en
Publisher: CRC Press
Release Date : 2014-10-27
Quantitative Graph Theory written by Matthias Dehmer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-27 with Computers categories.
The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical technique
Line Graphs And Line Digraphs
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Author : Lowell W. Beineke
language : en
Publisher: Springer Nature
Release Date : 2021-10-29
Line Graphs And Line Digraphs written by Lowell W. Beineke and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-29 with Mathematics categories.
In the present era dominated by computers, graph theory has come into its own as an area of mathematics, prominent for both its theory and its applications. One of the richest and most studied types of graph structures is that of the line graph, where the focus is more on the edges of a graph than on the vertices. A subject worthy of exploration in itself, line graphs are closely connected to other areas of mathematics and computer science. This book is unique in its extensive coverage of many areas of graph theory applicable to line graphs. The book has three parts. Part I covers line graphs and their properties, while Part II looks at features that apply specifically to directed graphs, and Part III presents generalizations and variations of both line graphs and line digraphs. Line Graphs and Line Digraphs is the first comprehensive monograph on the topic. With minimal prerequisites, the book is accessible to most mathematicians and computer scientists who have had an introduction graph theory, and will be a valuable reference for researchers working in graph theory and related fields.
Threshold Graphs And Related Topics
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Author : N.V.R. Mahadev
language : en
Publisher: Elsevier
Release Date : 1995-09-13
Threshold Graphs And Related Topics written by N.V.R. Mahadev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-13 with Mathematics categories.
Threshold graphs have a beautiful structure and possess many important mathematical properties. They have applications in many areas including computer science and psychology. Over the last 20 years the interest in threshold graphs has increased significantly, and the subject continues to attract much attention. The book contains many open problems and research ideas which will appeal to graduate students and researchers interested in graph theory. But above all Threshold Graphs and Related Topics provides a valuable source of information for all those working in this field.