Matching Minors In Bipartite Graphs

Author : Wiederrecht, Sebastian
Publisher : Universitätsverlag der TU Berlin
Page : 486 pages
File Size : 54,9 Mb
Release : 2022-04-19
Category : Computers
ISBN : 9783798332522

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Matching minors in bipartite graphs by Wiederrecht, Sebastian Pdf

In this thesis we adapt fundamental parts of the Graph Minors series of Robertson and Seymour for the study of matching minors and investigate a connection to the study of directed graphs. We develope matching theoretic to established results of graph minor theory: We characterise the existence of a cross over a conformal cycle by means of a topological property. Furthermore, we develope a theory for perfect matching width, a width parameter for graphs with perfect matchings introduced by Norin. here we show that the disjoint alternating paths problem can be solved in polynomial time on graphs of bounded width. Moreover, we show that every bipartite graph with high perfect matching width must contain a large grid as a matching minor. Finally, we prove an analogue of the we known Flat Wall theorem and provide a qualitative description of all bipartite graphs which exclude a fixed matching minor. In der vorliegenden Arbeit werden fundamentale Teile des Graphminorenprojekts von Robertson und Seymour für das Studium von Matching Minoren adaptiert und Verbindungen zur Strukturtheorie gerichteter Graphen aufgezeigt. Wir entwickeln matchingtheoretische Analogien zu etablierten Resultaten des Graphminorenprojekts: Wir charakterisieren die Existenz eines Kreuzes über einem konformen Kreis mittels topologischer Eigenschaften. Weiter entwickeln wir eine Theorie zu perfekter Matchingweite, einem Weiteparameter für Graphen mit perfekten Matchings, der von Norin eingeführt wurde. Hier zeigen wir, dass das Disjunkte Alternierende Pfade Problem auf bipartiten Graphen mit beschränkter Weite in Polynomialzeit lösbar ist. Weiter zeigen wir, dass jeder bipartite Graph mit hoher perfekter Matchingweite ein großes Gitter als Matchingminor enthalten muss. Schließlich zeigen wir ein Analogon des bekannten Flat Wall Theorem und geben eine qualitative Beschreibung aller bipartiter Graphen an, die einen festen Matching Minor ausschließen.

Author : Ignasi Sau,Dimitrios M. Thilikos
Publisher : Springer Nature
Page : 394 pages
File Size : 51,6 Mb
Release : 2019-09-11
Category : Mathematics
ISBN : 9783030307868

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Graph-Theoretic Concepts in Computer Science by Ignasi Sau,Dimitrios M. Thilikos Pdf

This book constitutes the revised papers of the 45th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2019, held in Vall de Núria, Spain, in June 2019. The 29 full papers presented in this volume were carefully reviewed and selected from 87 submissions. They cover a wide range of areas, aiming at connecting theory and applications by demonstrating how graph-theoretic concepts can be applied in various areas of computer science. Another focus is on presenting recent results and on identifying and exploring promising directions of future research.

Author : Hatzel, Meike
Publisher : Universitätsverlag der TU Berlin
Page : 294 pages
File Size : 44,6 Mb
Release : 2023-05-23
Category : Computers
ISBN : 9783798332911

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Dualities in graphs and digraphs by Hatzel, Meike Pdf

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.

Author : Jaroslav Nešetřil,Guillem Perarnau,Juanjo Rué,Oriol Serra
Publisher : Springer Nature
Page : 875 pages
File Size : 46,5 Mb
Release : 2021-08-23
Category : Mathematics
ISBN : 9783030838232

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Extended Abstracts EuroComb 2021 by Jaroslav Nešetřil,Guillem Perarnau,Juanjo Rué,Oriol Serra Pdf

This book collects the extended abstracts of the accepted contributions to EuroComb21. A similar book is published at every edition of EuroComb (every two years since 2001) collecting the most recent advances in combinatorics, graph theory, and related areas. It has a wide audience in the areas, and the papers are used and referenced broadly.

Author : Cláudio L. Lucchesi
Publisher : Springer Nature
Page : 584 pages
File Size : 54,6 Mb
Release : 2024
Category : Electronic books
ISBN : 9783031475047

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Perfect Matchings by Cláudio L. Lucchesi Pdf

Author : M.D. Plummer,L. Lovász
Publisher : Elsevier
Page : 543 pages
File Size : 42,8 Mb
Release : 1986-06-01
Category : Mathematics
ISBN : 0080872328

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Matching Theory by M.D. Plummer,L. Lovász Pdf

This study of matching theory deals with bipartite matching, network flows, and presents fundamental results for the non-bipartite case. It goes on to study elementary bipartite graphs and elementary graphs in general. Further discussed are 2-matchings, general matching problems as linear programs, the Edmonds Matching Algorithm (and other algorithmic approaches), f-factors and vertex packing.

Author : Marek Karpiński,Wojciech Rytter
Publisher : Oxford University Press
Page : 228 pages
File Size : 54,6 Mb
Release : 1998
Category : Computers
ISBN : 0198501625

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Fast Parallel Algorithms for Graph Matching Problems by Marek Karpiński,Wojciech Rytter Pdf

The matching problem is central to graph theory and the theory of algorithms. This book provides a comprehensive and straightforward introduction to the basic methods for designing efficient parallel algorithms for graph matching problems. Written for students at the beginning graduate level, the exposition is largely self-contained and example-driven; prerequisites have been kept to a minimum by including relevant background material. The book contains full details of several new techniques and will be of interest to researchers in computer science, operations research, discrete mathematics, and electrical engineering. The main theoretical tools are presented in three independent chapters, devoted to combinatorial tools, probabilistic tools, and algebraic tools. One of the goals of the book is to show how these three approaches can be combined to develop efficient parallel algorithms. The book represents a meeting point of interesting algorithmic techniques and opens up new algebraic and geometric areas.

Author : Bruce A. Reed,Claudia L. Linhares-Sales
Publisher : Springer Science & Business Media
Page : 357 pages
File Size : 43,8 Mb
Release : 2006-05-17
Category : Mathematics
ISBN : 9780387224442

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Recent Advances in Algorithms and Combinatorics by Bruce A. Reed,Claudia L. Linhares-Sales Pdf

Excellent authors, such as Lovasz, one of the five best combinatorialists in the world; Thematic linking that makes it a coherent collection; Will appeal to a variety of communities, such as mathematics, computer science and operations research

Author : Daniël Paulusma,Bernard Ries
Publisher : Springer Nature
Page : 491 pages
File Size : 50,6 Mb
Release : 2023-09-22
Category : Mathematics
ISBN : 9783031433801

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Graph-Theoretic Concepts in Computer Science by Daniël Paulusma,Bernard Ries Pdf

This volume constitutes the thoroughly refereed proceedings of the 49th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2023. The 33 full papers presented in this volume were carefully reviewed and selected from a total of 116 submissions. The WG 2022 workshop aims to merge theory and practice by demonstrating how concepts from graph theory can be applied to various areas in computer science, or by extracting new graph theoretic problems from applications.

Author : Armen S. Asratian,Tristan M. J. Denley,Roland Häggkvist
Publisher : Cambridge University Press
Page : 283 pages
File Size : 43,8 Mb
Release : 1998-07-13
Category : Mathematics
ISBN : 052159345X

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Bipartite Graphs and Their Applications by Armen S. Asratian,Tristan M. J. Denley,Roland Häggkvist Pdf

This is the first book which deals solely with bipartite graphs. Together with traditional material, the reader will also find many new and unusual results. Essentially all proofs are given in full; many of these have been streamlined specifically for this text. Numerous exercises of all standards have also been included. The theory is illustrated with many applications especially to problems in timetabling, Chemistry, Communication Networks and Computer Science. For the most part the material is accessible to any reader with a graduate understanding of mathematics. However, the book contains advanced sections requiring much more specialized knowledge, which will be of interest to specialists in combinatorics and graph theory.

Author : Reinhard Diestel
Publisher : Springer-Verlag, © Reinhard Diestel
Page : 447 pages
File Size : 55,8 Mb
Release : 2017-02-01
Category : Electronic
ISBN : 9783961340057

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Graph Theory by Reinhard Diestel Pdf

Professional electronic edition available from http://diestel-graph-theory.com/professional.html This standard textbook of modern graph theory, now in its fifth edition, combines the authority of a classic with the engaging freshness of style that is the hallmark of active mathematics. It covers the core material of the subject with concise yet reliably complete proofs, while offering glimpses of more advanced methods in each field by one or two deeper results, again with proofs given in full detail. The book can be used as a reliable text for an introductory course, as a graduate text, and for self-study. New in this 5th edition: Sections on tangles and tree-width, on tree packing and covering, and on topological spaces as inverse limits of finite graphs. Several new proofs of classical theorems. Many new exercises. From the reviews: “This outstanding book cannot be substituted with any other book on the present textbook market. It has every chance of becoming the standard textbook for graph theory.” Acta Scientiarum Mathematicarum "Deep, clear, wonderful. This is a serious book about the heart of graph theory. It has depth and integrity." Persi Diaconis & Ron Graham, SIAM Review “The book has received a very enthusiastic reception, which it amply deserves. A masterly elucidation of modern graph theory.” Bulletin of the Institute of Combinatorics and its Applications “Succeeds dramatically… a hell of a good book.” MAA Reviews “A highlight of the book is what is by far the best account in print of the Seymour-Robertson theory of graph minors.” Mathematika “…like listening to someone explain mathematics.” Bulletin of the AMS

Author : Roberto Tamassia,Ioannis G. Tollis
Publisher : World Scientific
Page : 439 pages
File Size : 45,9 Mb
Release : 2002
Category : Mathematics
ISBN : 9789810249267

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Graph Algorithms and Applications I by Roberto Tamassia,Ioannis G. Tollis Pdf

This book contains volumes 1-3 of the Journal of Graph Algorithms and Applications (JGAA). Topics of interest include design and analysis of graph algorithms, experiences with graph algorithms, and applications of graph algorithms. JGAA is supported by distinguished advisory and editorial boards, has high scientific standards, and takes advantage of current electronic document technology. The electronic version of JGAA is available on the Web at http: //www.cs.brown.edu/publications/jgaa/

Author : Roberto Tamassia,Ioannis G Tollis
Publisher : World Scientific
Page : 440 pages
File Size : 40,7 Mb
Release : 2002-03-11
Category : Computers
ISBN : 9789814488761

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Graph Algorithms and Applications I by Roberto Tamassia,Ioannis G Tollis Pdf

This book contains volumes 1–3 of the Journal of Graph Algorithms and Applications (JGAA). Topics of interest include design and analysis of graph algorithms, experiences with graph algorithms, and applications of graph algorithms. JGAA is supported by distinguished advisory and editorial boards, has high scientific standards, and takes advantage of current electronic document technology. The electronic version of JGAA is available on the Web at http://www.cs.brown.edu/publications/jgaa/. Contents:Volume 1:2-Layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms (M Jünger & P Mutzel)Optimal Algorithms to Embed Trees in a Point Set (P Bose et al.)Low-degree Graph Partitioning via Local Search with Applications to Constraint Satisfaction, Max Cut, and Coloring (M M Halldórsson & H C Lau)Volume 2:Algorithms for Cluster Busting in Anchored Graph Drawing (K A Lyons et al.)A Broadcasting Algorithm with Time and Message Optimum on Arrangement Graphs (L Bai et al.)A Visibility Representation for Graphs in Three Dimensions (P Bose et al.)Scheduled Hot-Potato Routing (J Naor et al.)Treewidth and Minimum Fill-in on d-trapezoid Graphs (H L Bodlaender et al.)Memory Paging for Connectivity and Path Problems in Graphs (E Feuerstein & A Marchetti-Spaccamela)New Lower Bounds for Orthogonal Drawings (T C Biedl)Rectangle-visibility Layouts of Unions and Products of Trees (A M Dean & J P Hutchinson)Volume 3:Edge-Coloring and f-Coloring for Various Classes of Graphs (X Zhou & T Nishizeki)Experimental Comparison of Graph Drawing Algorithms for Cubic Graphs (T Calamoneri et al.)Subgraph Isomorphism in Planar Graphs and Related Problems (D Eppstein)Guest Editors' Introduction (G Di Battista & P Mutzel)Drawing Clustered Graphs on an Orthogonal Grid (P Eades et al.)A Linear Algorithm for Bend-Optimal Orthogonal Drawings of Triconnected Cubic Plane Graphs (M S Rahman et al.)Bounds for Orthogonal 3-D Graph Drawing (T Biedl et al.)Algorithms for Incremental Orthogonal Graph Drawing in Three Dimensions (A Papakostas & I G Tollis) Readership: Researchers and professionals in theoretical computer science, computer engineering and combinatorics & graph theory. Keywords:Graphs;Networks;Graph Algorithms;Data Structures;Analysis of Algorithms;Experimental Studies;Algorithm Engineering;Information Visualization;Telecommunication Networks;Scheduling;Graph Drawing;Graph Theory

Author : Tianyuan Xiao,Lin Zhang,Shiwei Ma
Publisher : Springer
Page : 462 pages
File Size : 52,7 Mb
Release : 2012-10-08
Category : Computers
ISBN : 9783642343810

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System Simulation and Scientific Computing by Tianyuan Xiao,Lin Zhang,Shiwei Ma Pdf

The Three-Volume-Set CCIS 323, 324, 325 (AsiaSim 2012) together with the Two-Volume-Set CCIS 326, 327 (ICSC 2012) constitutes the refereed proceedings of the Asia Simulation Conference, AsiaSim 2012, and the International Conference on System Simulation, ICSC 2012, held in Shanghai, China, in October 2012. The 267 revised full papers presented were carefully reviewed and selected from 906 submissions. The papers are organized in topical sections on modeling theory and technology; modeling and simulation technology on synthesized environment and virtual reality environment; pervasive computing and simulation technology; embedded computing and simulation technology; verification, validation and accreditation technology; networked modeling and simulation technology; modeling and simulation technology of continuous system, discrete system, hybrid system, and intelligent system; high performance computing and simulation technology; cloud simulation technology; modeling and simulation technology of complex system and open, complex, huge system; simulation based acquisition and virtual prototyping engineering technology; simulator; simulation language and intelligent simulation system; parallel and distributed software; CAD, CAE, CAM, CIMS, VP, VM, and VR; visualization; computing and simulation applications in science and engineering; computing and simulation applications in management, society and economics; computing and simulation applications in life and biomedical engineering; computing and simulation applications in energy and environment; computing and simulation applications in education; computing and simulation applications in military field; computing and simulation applications in medical field.

Author : Jon Lee,Giovanni Rinaldi,A. Ridha Mahjoub
Publisher : Springer
Page : 430 pages
File Size : 43,6 Mb
Release : 2018-07-17
Category : Computers
ISBN : 9783319961514

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Combinatorial Optimization by Jon Lee,Giovanni Rinaldi,A. Ridha Mahjoub Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the 5th International Symposium on Combinatorial Optimization, ISCO 2018, held in Marrakesh, Marocco, in April 2018. The 35 revised full papers presented in this book were carefully reviewed and selected from 75 submissions. The symposium aims to bring together researchers from all the communities related to combinatorial optimization, including algorithms and complexity, mathematical programming and operations research.