Convexity In Graphs
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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.
Convexity And Graph Theory
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Author : M. Rosenfeld
language : en
Publisher: Elsevier
Release Date : 1984-01-01
Convexity And Graph Theory written by M. Rosenfeld and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Mathematics categories.
Among the participants discussing recent trends in their respective fields and in areas of common interest in these proceedings are such world-famous geometers as H.S.M. Coxeter, L. Danzer, D.G. Larman and J.M. Wills, and equally famous graph-theorists B. Bollobás, P. Erdös and F. Harary. In addition to new results in both geometry and graph theory, this work includes articles involving both of these two fields, for instance ``Convexity, Graph Theory and Non-Negative Matrices'', ``Weakly Saturated Graphs are Rigid'', and many more. The volume covers a broad spectrum of topics in graph theory, geometry, convexity, and combinatorics. The book closes with a number of abstracts and a collection of open problems raised during the conference.
Convexity In Graphs
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Author : John L. Pfaltz
language : en
Publisher:
Release Date : 1968
Convexity In Graphs written by John L. Pfaltz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Computer graphics categories.
A natural concept of convexity for directed graphs is introduced, and properties of the lattice of convex subgraphs of a graph are studied. The extent to which this lattice determines the graph is established, and conditions for a lattice to be a convex subgraph lattice are investigated. The concept of a lower semi-homomorphism is defined for lattices; it is shown that such mappings preserve basic properties of convex subgraph lattices, and that on such lattices, they are uniquely determined by their kernels. Graph homomorphisms which preserve convexity are also studied, with emphasis on their relationship to lower semi-homomorphisms of the convex subgraph lattice. Homomorphisms which 'contract' subgraphs (which are analogous to the rewriting rules of context-sensitive phrase structure grammars) are briefly considered. Finally, a concept of local convexity for directed graphs is introduced. (Author).
Convexity In Graphs
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Author : John L. Pfaltz
language : en
Publisher:
Release Date : 1968
Convexity In Graphs written by John L. Pfaltz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Convex domains categories.
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 And Hypergraphs
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Author : Farber, Martin
language : en
Publisher:
Release Date : 1983
Convexity In Graphs And Hypergraphs written by Farber, Martin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Convex sets 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.
Convexity And Discrete Geometry Including Graph Theory
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Author : Karim Adiprasito
language : en
Publisher: Springer
Release Date : 2016-05-02
Convexity And Discrete Geometry Including Graph Theory written by Karim Adiprasito and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-02 with Mathematics categories.
This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
An Algorithmic Theory Of Numbers Graphs And Convexity
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Author : Laszlo Lovasz
language : en
Publisher: SIAM
Release Date : 1987-01-01
An Algorithmic Theory Of Numbers Graphs And Convexity written by Laszlo Lovasz and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-01-01 with Mathematics categories.
Studies two algorithms in detail: the ellipsoid method and the simultaneous diophantine approximation method.
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.