The Asymptotic Existence Of Graph Decompositions With Loops

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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.

Asymptotic Existence Of Decompositions Of Edge Colored Graphs And Hypergraphs

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Author : Anna Draganova Draganova
language : en
Publisher:
Release Date : 2006

Asymptotic Existence Of Decompositions Of Edge Colored Graphs And Hypergraphs written by Anna Draganova Draganova and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.

The most general setting of an asymptotic existence question of decompositions of complete graphs is completed, the study of which has been a subject of series of papers since the 1970s. Denote by Kl1,l2 ,...,lr n the complete directed graph on r colors and n vertices with li directed edges of color i between any ordered pair of vertices. For any given family of digraphs G , we find necessary and asymptotically sufficient conditions on n for the existence of decompositions of Kl1,l2 ,...,lr n into subgraphs isomorphic to digraphs in G . Our main result provides a convenient set-up for numerous problems in combinatorial design theory; we use it to give a short proof for the asymptotic existence of resolvable (v,k, l )-BIBDs for any value of l . The asymptotic existence of signed (H,r)-designs is examined by considering decompositions of t-uniform hypergraphs.

Orthogonal Decompositions And Functional Limit Theorems For Random Graph Statistics

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Author : Svante Janson
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Orthogonal Decompositions And Functional Limit Theorems For Random Graph Statistics written by Svante Janson 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 1994 with Mathematics categories.

We define an orthogonal basis in the space of real-valued functions of a random graph, and prove a functional limit theorem for this basis. Limit theorems for other functions then follow by decomposition. The results include limit theorems for the two random graph models [italic]G[subscript italic]n, [subscript italic]p and [italic]G[subscript italic]n, [subscript italic]m as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Both normal and non-normal limits are obtained. As examples, applications are given to subgraph counts and to vertex degrees.

New Advances In Designs Codes And Cryptography

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Author : Charles J. Colbourn
language : en
Publisher: Springer Nature
Release Date :

New Advances In Designs Codes And Cryptography written by Charles J. Colbourn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Surveys In Combinatorics 1999

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Author : J. D. Lamb
language : en
Publisher: Cambridge University Press
Release Date : 1999-07

Surveys In Combinatorics 1999 written by J. D. Lamb and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-07 with Mathematics categories.

This volume, first published in 1999, is a valuable resource on combinatorics for graduate students and researchers.

Leveraging Applications Of Formal Methods Verification And Validation

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Author : Tiziana Margaria
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-11-05

Leveraging Applications Of Formal Methods Verification And Validation written by Tiziana Margaria 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 2008-11-05 with Computers categories.

This volume contains the conference proceedings of ISoLA 2008, the Third International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, which was held in Porto Sani (Kassandra, Chalkidiki), Greece during October 13–15, 2008, sponsored by EASST and in cooperation with the IEEE Technical Committee on Complex Systems. Following the tradition of its forerunners in 2004 and 2006 in Cyprus, and the ISoLA Workshops in Greenbelt (USA) in 2005 and in Poitiers (France) in 2007, ISoLA 2008 provided a forum for developers, users, and researchers to discuss issues related to the adoption and use of rigorous tools and methods for the specification, analysis, verification, certification, construction, test, and maintenance of systems from the point of view of their different application domains. Thus, the ISoLA series of events serves the purpose of bridging the gap between designers and developers of rigorous tools, and users in engineering and in other disciplines, and to foster and exploit synergetic relationships among scientists, engineers, software developers, decision makers, and other critical thinkers in companies and organizations. In p- ticular, by providing a venue for the discussion of common problems, requirements, algorithms, methodologies, and practices, ISoLA aims at supporting researchers in their quest to improve the utility, reliability, flexibility, and efficiency of tools for building systems, and users in their search for adequate solutions to their problems.

Random Graphs Geometry And Asymptotic Structure

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Author : Michael Krivelevich
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-25

Random Graphs Geometry And Asymptotic Structure written by Michael Krivelevich and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-25 with Mathematics categories.

A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.

Hybrid Systems Computation And Control

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Author : Rupak Majumdar
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-27

Hybrid Systems Computation And Control written by Rupak Majumdar 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 2009-03-27 with Computers categories.

This book constitutes the refereed proceedings of the 12th International Conference on Hybrid Systems: Computation and Control, HSCC 2009, held in San Francisco, CA, USA, in April 2009. The 30 revised full papers and 10 revised short papers presented were carefully reviewed and selected from numerous submissions for inclusion in the book. The papers focus on research in embedded reactive systems involving the interplay between symbolic/discrete and continuous dynamical behaviors and feature the latest developments of applications and theoretical advancements in the analysis, design, control, optimization, and implementation of hybrid systems.

Triple Systems

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Author : Charles J. Colbourn
language : en
Publisher: Oxford University Press
Release Date : 1999

Triple Systems written by Charles J. Colbourn and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Computers categories.

Among the simplest combinatorial designs, triple systems have diverse applications in coding theory, cryptography, computer science, and statistics. This book provides a systematic and comprehensive treatment of this rich area of mathematics.