Convexity In Graphs Vertex Order Characterisations And Graph Searching
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Convexity In Graphs Vertex Order Characterisations And Graph Searching
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Author : Jesse Beisegel
language : en
Publisher:
Release Date : 2020
Convexity In Graphs Vertex Order Characterisations And Graph Searching written by Jesse Beisegel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Convex domains categories.
Convexity In Graphs
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Author : Jesse Beisegel
language : en
Publisher:
Release Date : 2020
Convexity In Graphs written by Jesse Beisegel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Graph Convexity And Vertex Orderings
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Author : Rachel Jean Selma Anderson
language : en
Publisher:
Release Date : 2014
Graph Convexity And Vertex Orderings written by Rachel Jean Selma Anderson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
In discrete mathematics, a convex space is an ordered pair (V,M) where M is a family of subsets of a finite set V , such that: ? ?M, V ?M, and Mis closed under intersection. The elements of M are called convex sets. For a set S ? V , the convex hull of S is the smallest convex set that contains S. A point x of a convex set X is an extreme point of X if X\{x} is also convex. A convex space (V,M) with the property that every convex set is the convex hull of its extreme points is called a convex geometry. A graph G has a P-elimination ordering if an ordering v1, v2, ..., vn of the vertices exists such that vi has property P in the graph induced by vertices vi, vi+1, ..., vn for all i = 1, 2, ...,n. Farber and Jamison [18] showed that for a convex geometry (V,M),X ?M if and only if there is an ordering v1, v2, ..., vk of the points of V ? X such that vi is an extreme point of {vi, vi+1, ..., vk}? X for each i = 1, 2, ...,k. With these concepts in mind, this thesis surveys the literature and summarizes results regarding graph convexities and elimination orderings. These results include classifying graphs for which different types of convexities give convex geometries, and classifying graphs for which different vertex ordering algorithms result in a P-elimination ordering, for P the characteristic property of the extreme points of the convexity. We consider the geodesic, monophonic, m3, 3-Steiner and 3-monophonic convexities, and the vertex ordering algorithms LexBFS, MCS, MEC and MCC. By considering LexDFS, a recently introduced vertex ordering algorithm of Corneil and Krueger [11], we obtain new results: these are characterizations of graphs for which all LexDFS orderings of all induced subgraphs are P-elimination orderings, for every characteristic property P of the extreme vertices for the convexities studied in this thesis.
Enumerating Digitally Convex Sets In Graphs
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Author : MacKenzie Carr
language : en
Publisher:
Release Date : 2020
Enumerating Digitally Convex Sets In Graphs written by MacKenzie Carr and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with categories.
Given a finite set V, a convexity, C, is a collection of subsets of V that contains both the empty set and the set V and is closed under intersections. The elements of C are called convex sets. We can define several different convexities on the vertex set of a graph. In particular, the digital convexity, originally proposed as a tool for processing digital images, is defined as follows: a subset S of V(G) is digitally convex if, for every vertex v in V(G), we have N[v] a subset of N[S] implies v in S. Or, in other words, each vertex v that is not in the digitally convex set S needs to have a private neighbour in the graph with respect to S. In this thesis, we focus on the generation and enumeration of digitally convex sets in several classes of graphs. We establish upper bounds on the number of digitally convex sets of 2-trees, k-trees and simple clique 2-trees, as well as conjecturing a lower bound on the number of digitally convex sets of 2-trees and a generalization to k-trees. For other classes of graphs, including powers of cycles and paths, and Cartesian products of complete graphs and of paths, we enumerate the digitally convex sets using recurrence relations. Finally, we enumerate the digitally convex sets of block graphs in terms of the number of blocks in the graph, rather than in terms of the order of the graph.
A Guide To Graph Algorithms
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Author : Ton Kloks
language : en
Publisher: Springer Nature
Release Date : 2022-02-22
A Guide To Graph Algorithms written by Ton Kloks and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-22 with Computers categories.
This book A Guide to Graph Algorithms offers high-quality content in the research area of graph algorithms and explores the latest developments in graph algorithmics. The reader will gain a comprehensive understanding of how to use algorithms to explore graphs. It is a collection of texts that have proved to be trend setters and good examples of that. The book aims at providing the reader with a deep understanding of the structural properties of graphs that are useful for the design of efficient algorithms. These algorithms have applications in finite state machine modelling, social network theory, biology, and mathematics. The book contains many exercises, some up at present-day research-level. The exercises encourage the reader to discover new techniques by putting things in a clear perspective. A study of this book will provide the reader with many powerful tools to model and tackle problems in real-world scenarios.
Geometry Intuitive Discrete And Convex
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Author : Imre Bárány
language : en
Publisher: Springer
Release Date : 2015-04-09
Geometry Intuitive Discrete And Convex written by Imre Bárány and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-04-09 with Mathematics categories.
The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, László Fejes Tóth, on the 99th anniversary of his birth. Each article reviews recent progress in an important field in intuitive, discrete, and convex geometry. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by László Fejes Tóth.
Computing And Combinatorics
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Author : Bin Fu
language : en
Publisher: Springer
Release Date : 2011-07-18
Computing And Combinatorics written by Bin Fu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-18 with Computers categories.
This book constitutes the refereed proceedings of the 17th Annual International Conference on Computing and Combinatorics, held in Dallas, TX, USA, in August 2011. The 54 revised full papers presented were carefully reviewed and selected from 136 submissions. Topics covered are algorithms and data structures; algorithmic game theory and online algorithms; automata, languages, logic, and computability; combinatorics related to algorithms and complexity; complexity theory; computational learning theory and knowledge discovery; cryptography, reliability and security, and database theory; computational biology and bioinformatics; computational algebra, geometry, and number theory; graph drawing and information visualization; graph theory, communication networks, and optimization; parallel and distributed computing.
Graph Theoretic Concepts In Computer Science
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Author : Andreas Brandstädt
language : en
Publisher: Springer
Release Date : 2018-09-01
Graph Theoretic Concepts In Computer Science written by Andreas Brandstädt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-01 with Computers categories.
This book constitutes the revised selected papers of the 44th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2018, held in Cottbus, Germany, in June 2018. The 30 full papers presented in this volume were carefully reviewed and selected from 66 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.
Graph Theory And Sparse Matrix Computation
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Author : Alan George
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Graph Theory And Sparse Matrix Computation written by Alan George 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 2012-12-06 with Mathematics categories.
When reality is modeled by computation, matrices are often the connection between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix, the better the answer, however, efficiency demands that every possible advantage be exploited. The articles in this volume are based on recent research on sparse matrix computations. This volume looks at graph theory as it connects to linear algebra, parallel computing, data structures, geometry, and both numerical and discrete algorithms. The articles are grouped into three general categories: graph models of symmetric matrices and factorizations, graph models of algorithms on nonsymmetric matrices, and parallel sparse matrix algorithms. This book will be a resource for the researcher or advanced student of either graphs or sparse matrices; it will be useful to mathematicians, numerical analysts and theoretical computer scientists alike.
Geodesic Convexity In Graphs
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Author : Ignacio M. Pelayo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-06
Geodesic Convexity In Graphs written by Ignacio M. Pelayo 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 2013-09-06 with Mathematics categories.
Geodesic Convexity in Graphs is devoted to the study of the geodesic convexity on finite, simple, connected graphs. The first chapter includes the main definitions and results on graph theory, metric graph theory and graph path convexities. The following chapters focus exclusively on the geodesic convexity, including motivation and background, specific definitions, discussion and examples, results, proofs, exercises and open problems. The main and most studied parameters involving geodesic convexity in graphs are both the geodetic and the hull number which are defined as the cardinality of minimum geodetic and hull set, respectively. This text reviews various results, obtained during the last one and a half decade, relating these two invariants and some others such as convexity number, Steiner number, geodetic iteration number, Helly number, and Caratheodory number to a wide range a contexts, including products, boundary-type vertex sets, and perfect graph families. This monograph can serve as a supplement to a half-semester graduate course in geodesic convexity but is primarily a guide for postgraduates and researchers interested in topics related to metric graph theory and graph convexity theory.