Graph Decompositions

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Graph Decompositions

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Author : Reinhard Diestel
language : en
Publisher: Oxford Science Publications
Release Date : 1990

Graph Decompositions written by Reinhard Diestel and has been published by Oxford Science Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Language Arts & Disciplines categories.

Graph Decompositions is the first book on a topic that belongs mainly to infinite graph theory. It offers a complete account of the theory of simplicial decompositions of graphs, from its origins in the 1930s right up to present-day research.In addition to being one of the most important tools in infinite graph theory, simplicial decompositions may be seen as a model for any kind of structural graph decomposition. The currently topical tree-decompositions, for example, have their origin in simplicial decompositions.The text is centred around a few guiding problems and concepts, such as the existence and the uniqueness problem of simplicial decompositions into primes, or the concept of excluded minors as a means of identifying a desired structure.It attempts to give as authentic a picture as possible ofresearch in progress. To this end, it includes discussions of examples, proof strategies on the formation of new concepts, as well as numerous exercises and open problems.Graph Decompositions should prove attractive to any graph theorist or other mathematician interested in a new area of research, as well as to the advanced student looking for a lively and inspiring account of how such research evolves.

Decompositions Of Graphs

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Author : Juraj Bosák
language : en
Publisher: Taylor & Francis US
Release Date : 1990

Decompositions Of Graphs written by Juraj Bosák and has been published by Taylor & Francis US this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.

Graph Theory And Decomposition

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Author : Jomon Kottarathil
language : en
Publisher: CRC Press
Release Date : 2024-04-10

Graph Theory And Decomposition written by Jomon Kottarathil and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-10 with Mathematics categories.

The book Graph Theory and Decomposition covers major areas of the decomposition of graphs. It is a three-part reference book with nine chapters that is aimed at enthusiasts as well as research scholars. It comprehends historical evolution and basic terminologies, and it deliberates on decompositions into cyclic graphs, such as cycle, digraph, and K4-e decompositions. In addition to determining the pendant number of graphs, it has a discourse on decomposing a graph into acyclic graphs like general tree, path, and star decompositions. It summarises another recently developed decomposition technique, which decomposes the given graph into multiple types of subgraphs. Major conjectures on graph decompositions are elaborately discussed. It alludes to a comprehensive bibliography that includes over 500 monographs and journal articles. It includes more than 500 theorems, around 100 definitions, 56 conjectures, 40 open problems, and an algorithm. The index section facilitates easy access to definitions, major conjectures, and named theorems. Thus, the book Graph Theory and Decomposition will be a great asset, we hope, in the field of decompositions of graphs and will serve as a reference book for all who are passionate about graph theory.

Localized Structure In Graph Decompositions

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Author : Flora Caroline Bowditch
language : en
Publisher:
Release Date : 2019

Localized Structure In Graph Decompositions written by Flora Caroline Bowditch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.

Let v ∈ Z+ and G be a simple graph. A G-decomposition of Kv is a collection F={F1,F2,...,Ft} of subgraphs of Kv such that every edge of Kv occurs in exactlyone of the subgraphs and every graph Fi ∈ F is isomorphic to G. A G-decomposition of Kv is called balanced if each vertex of Kv occurs in the same number of copies of G. In 2011, Dukes and Malloch provided an existence theory for balanced G-decompositions of Kv. Shortly afterwards, Bonisoli, Bonvicini, and Rinaldi introduced degree- and orbit-balanced G-decompositions. Similar to balanced decompositions,these two types of G-decompositions impose a local structure on the vertices of Kv. In this thesis, we will present an existence theory for degree- and orbit-balanced G-decompositions of Kv. To do this, we will first develop a theory for decomposing Kv into copies of G when G contains coloured loops. This will be followed by a brief discussion about the applications of such decompositions. Finally, we will explore anextension of this problem where Kv is decomposed into a family of graphs. We will examine the complications that arise with families of graphs and provide results for a few special cases.

Methods Of Graph Decompositions

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Author : DR VADIM. SKUMS ZVEROVICH (DR PAVEL.)
language : en
Publisher:
Release Date : 2024-06-15

Methods Of Graph Decompositions written by DR VADIM. SKUMS ZVEROVICH (DR PAVEL.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-15 with Mathematics categories.

This book discusses some methods of graph decompositions, which are highly instrumental when dealing with a number of fundamental problems of graph theory. The presented topics are united by the role played in their development by Professor Regina Tyshkevich, and the book is a tribute to her memory.

Graph Decompositions Theta Graphs And Related Graph Labelling Techniques

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Author : Andrew Blinco
language : en
Publisher:
Release Date : 2003

Graph Decompositions Theta Graphs And Related Graph Labelling Techniques written by Andrew Blinco and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Graph labelings categories.

Graph Decompositions

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Author : Lisa A. Lister
language : en
Publisher:
Release Date : 1997

Graph Decompositions written by Lisa A. Lister and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Decomposition (Mathematics) categories.

The Asymptotic Existence Of Graph Decompositions With Loops

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Author : Amanda Malloch
language : en
Publisher:
Release Date : 2009

The Asymptotic Existence Of Graph Decompositions With Loops written by Amanda Malloch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.

Let v [greater than or equal to] k [greater than or equal to] 1 and lamda [greater than or equal to] 0 be integers and G be a graph with n vertices, m edges, and no multiple edges. A (v, k, lambda) block design is a collection Beta of k-subsets of a v-set X in which every unordered pair of elements in X is contained in exactly lambda of the subsets in Beta. A (G-decomposition, or (v, G, lambda) graph design, is a collection H1, H2 ..., Ht of subgraphs of Kv (the complete graph on v vertices) such that each edge of Kv is an edge of exactly lambda of the subgraphs Hi and each of the subgraphs Hi is isomorphic to G.A famous result by Wilson says that for a fixed graph G and integer lambda, there exists a (v, G, lambda) graph design for all sufficiently large integers v satisfying certain necessary conditions. In this thesis, we extend this result to include the case of loops in G. As a consequence, one obtains asymptotic existence of equireplicate graph designs for values of v satisfying certain necessary conditions, where a graph design is called equireplicate if each vertex of Kv occurs in the same number of subgraphs Hi of the decomposition.

The Asymptotic Existence Of Graph Decompositions With Loops

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Author :
language : en
Publisher:
Release Date : 2008

The Asymptotic Existence Of Graph Decompositions With Loops written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Let v [greater than or equal to] k [greater than or equal to] 1 and lamda [greater than or equal to] 0 be integers and G be a graph with n vertices, m edges, and no multiple edges. A (v, k, lambda) block design is a collection Beta of k-subsets of a v-set X in which every unordered pair of elements in X is contained in exactly lambda of the subsets in Beta. A (G-decomposition, or (v, G, lambda) graph design, is a collection H1, H2 ..., Ht of subgraphs of Kv (the complete graph on v vertices) such that each edge of Kv is an edge of exactly lambda of the subgraphs Hi and each of the subgraphs Hi is isomorphic to G.A famous result by Wilson says that for a fixed graph G and integer lambda, there exists a (v, G, lambda) graph design for all sufficiently large integers v satisfying certain necessary conditions. In this thesis, we extend this result to include the case of loops in G. As a consequence, one obtains asymptotic existence of equireplicate graph designs for values of v satisfying certain necessary conditions, where a graph design is called equireplicate if each vertex of Kv occurs in the same number of subgraphs Hi of the decomposition.

Graph Decompositions And Monadic Second Order Logic

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Author : Jonathan D. Adler
language : en
Publisher:
Release Date : 2008

Graph Decompositions And Monadic Second Order Logic written by Jonathan D. Adler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Abstract: A tree decomposition is a tool which allows for analysis of the underlying tree structure of graphs which are not trees. Given a class of graphs with bounded tree width, many NP-complete problems can be computed in linear time for graphs in the class. Clique width of a graph G is a measure of the number of labels required to construct G using several particular graph operations. For any integer k, both the class of graphs with tree width at most k and the class of graphs with clique width at most k have a decidable monadic second order theory. In this paper we explore some recent results in applying these graph measures and their relation to monadic second order logic.