Cycles And Bridges In Graphs
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Cycles And Bridges In Graphs
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Author : Heinz-Jürgen Voss
language : en
Publisher: Springer
Release Date : 1991-08-31
Cycles And Bridges In Graphs written by Heinz-Jürgen Voss and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-08-31 with Mathematics categories.
Chromatic Graph Theory
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Author : Gary Chartrand
language : en
Publisher: CRC Press
Release Date : 2008-09-22
Chromatic Graph Theory written by Gary Chartrand and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-22 with Computers categories.
Beginning with the origin of the four color problem in 1852, the field of graph colorings has developed into one of the most popular areas of graph theory. Introducing graph theory with a coloring theme, Chromatic Graph Theory explores connections between major topics in graph theory and graph colorings as well as emerging topics. This self-contain
Bridge Graphs And The Carrier Poset For Biconnected Simple Graphs
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Author : Peter Washington Stephens
language : en
Publisher:
Release Date : 1993
Bridge Graphs And The Carrier Poset For Biconnected Simple Graphs written by Peter Washington Stephens and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Covering Walks In Graphs
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Author : Futaba Fujie
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-01-25
Covering Walks In Graphs written by Futaba Fujie 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 2014-01-25 with Mathematics categories.
Covering Walks in Graphs is aimed at researchers and graduate students in the graph theory community and provides a comprehensive treatment on measures of two well studied graphical properties, namely Hamiltonicity and traversability in graphs. This text looks into the famous Kӧnigsberg Bridge Problem, the Chinese Postman Problem, the Icosian Game and the Traveling Salesman Problem as well as well-known mathematicians who were involved in these problems. The concepts of different spanning walks with examples and present classical results on Hamiltonian numbers and upper Hamiltonian numbers of graphs are described; in some cases, the authors provide proofs of these results to illustrate the beauty and complexity of this area of research. Two new concepts of traceable numbers of graphs and traceable numbers of vertices of a graph which were inspired by and closely related to Hamiltonian numbers are introduced. Results are illustrated on these two concepts and the relationship between traceable concepts and Hamiltonian concepts are examined. Describes several variations of traceable numbers, which provide new frame works for several well-known Hamiltonian concepts and produce interesting new results.
Cycles And Rays
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Author : Gena Hahn
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-12-31
Cycles And Rays written by Gena Hahn 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 1989-12-31 with Mathematics categories.
What is the "archetypal" image that comes to mind when one thinks of an infinite graph? What with a finite graph - when it is thought of as opposed to an infinite one? What structural elements are typical for either - by their presence or absence - yet provide a common ground for both? In planning the workshop on "Cycles and Rays" it had been intended from the outset to bring infinite graphs to the fore as much as possible. There never had been a graph theoretical meeting in which infinite graphs were more than "also rans", let alone one in which they were a central theme. In part, this is a matter of fashion, inasmuch as they are perceived as not readily lending themselves to applications, in part it is a matter of psychology stemming from the insecurity that many graph theorists feel in the face of set theory - on which infinite graph theory relies to a considerable extent. The result is that by and large, infinite graph theorists know what is happening in finite graphs but not conversely. Lack of knowledge about infinite graph theory can also be found in authoritative l sources. For example, a recent edition (1987) of a major mathematical encyclopaedia proposes to ". . . restrict [itself] to finite graphs, since only they give a typical theory". If anything, the reverse is true, and needless to say, the graph theoretical world knows better. One may wonder, however, by how much.
Local Conditions For Cycles In Graphs
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Author : Jonas Granholm
language : en
Publisher: Linköping University Electronic Press
Release Date : 2019-05-06
Local Conditions For Cycles In Graphs written by Jonas Granholm and has been published by Linköping University Electronic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-06 with categories.
A Hamilton cycle in a graph is a cycle that passes through every vertex of the graph. A graph is called Hamiltonian if it contains such a cycle. The problem of determining if a graph is Hamiltonian has been studied extensively, and there are many known sufficient conditions for Hamiltonicity. A large portion of these conditions relate the degrees of vertices of the graph to the number of vertices in the entire graph, and thus they can only apply to a limited set of graphs with high edge density. In a series of papers, Asratian and Khachatryan developed local analogues of some of these criteria. These results do not suffer from the same drawbacks as their global counterparts, and apply to wider classes of graphs. In this thesis we study this approach of creating local conditions for Hamiltonicity, and use it to develop local analogues of some classic results. We also study how local criteria can influence other global properties of graphs. Finally, we will see how these local conditions can allow us to extend theorems on Hamiltonicity to infinite graphs.
Building Bridges Ii
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Author : Imre Bárány
language : en
Publisher: Springer Nature
Release Date : 2020-02-04
Building Bridges Ii written by Imre Bárány and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-04 with Mathematics categories.
This volume collects together research and survey papers written by invited speakers of the conference celebrating the 70th birthday of László Lovász. The topics covered include classical subjects such as extremal graph theory, coding theory, design theory, applications of linear algebra and combinatorial optimization, as well as recent trends such as extensions of graph limits, online or statistical versions of classical combinatorial problems, and new methods of derandomization. László Lovász is one of the pioneers in the interplay between discrete and continuous mathematics, and is a master at establishing unexpected connections, “building bridges” between seemingly distant fields. His invariably elegant and powerful ideas have produced new subfields in many areas, and his outstanding scientific work has defined and shaped many research directions in the last 50 years. The 14 contributions presented in this volume, all of which are connected to László Lovász's areas of research, offer an excellent overview of the state of the art of combinatorics and related topics and will be of interest to experienced specialists as well as young researchers.
Building Bridges
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Author : Martin Grötschel
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-28
Building Bridges written by Martin Grötschel 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 2010-05-28 with Mathematics categories.
Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is László Lovász, a scholar whose outstanding scientific work has defined and shaped many research directions in the last 40 years. A number of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at one of two conferences in August 2008 in Hungary, both celebrating Lovász’s 60th birthday, have contributed their latest research papers to this volume. This collection of articles offers an excellent view on the state of combinatorics and related topics and will be of interest for experienced specialists as well as young researchers.
Hamiltonian Cycle Problem And Markov Chains
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Author : Vivek S. Borkar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-23
Hamiltonian Cycle Problem And Markov Chains written by Vivek S. Borkar 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 2012-04-23 with Business & Economics categories.
This research monograph summarizes a line of research that maps certain classical problems of discrete mathematics and operations research - such as the Hamiltonian Cycle and the Travelling Salesman Problems - into convex domains where continuum analysis can be carried out. Arguably, the inherent difficulty of these, now classical, problems stems precisely from the discrete nature of domains in which these problems are posed. The convexification of domains underpinning these results is achieved by assigning probabilistic interpretation to key elements of the original deterministic problems. In particular, the approaches summarized here build on a technique that embeds Hamiltonian Cycle and Travelling Salesman Problems in a structured singularly perturbed Markov decision process. The unifying idea is to interpret subgraphs traced out by deterministic policies (including Hamiltonian cycles, if any) as extreme points of a convex polyhedron in a space filled with randomized policies. The above innovative approach has now evolved to the point where there are many, both theoretical and algorithmic, results that exploit the nexus between graph theoretic structures and both probabilistic and algebraic entities of related Markov chains. The latter include moments of first return times, limiting frequencies of visits to nodes, or the spectra of certain matrices traditionally associated with the analysis of Markov chains. However, these results and algorithms are dispersed over many research papers appearing in journals catering to disparate audiences. As a result, the published manuscripts are often written in a very terse manner and use disparate notation, thereby making it difficult for new researchers to make use of the many reported advances. Hence the main purpose of this book is to present a concise and yet easily accessible synthesis of the majority of the theoretical and algorithmic results obtained so far. In addition, the book discusses numerous open questions and problems that arise from this body of work and which are yet to be fully solved. The approach casts the Hamiltonian Cycle Problem in a mathematical framework that permits analytical concepts and techniques, not used hitherto in this context, to be brought to bear to further clarify both the underlying difficulty of NP-completeness of this problem and the relative exceptionality of truly difficult instances. Finally, the material is arranged in such a manner that the introductory chapters require very little mathematical background and discuss instances of graphs with interesting structures that motivated a lot of the research in this topic. More difficult results are introduced later and are illustrated with numerous examples.
Integer Flows And Cycle Covers Of Graphs
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Author : Cun-Quan Zhang
language : en
Publisher: CRC Press
Release Date : 1997-01-02
Integer Flows And Cycle Covers Of Graphs written by Cun-Quan Zhang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-02 with Mathematics categories.
Focuses on classical problems in graph theory, including the 5-flow conjectures, the edge-3-colouring conjecture, the 3-flow conjecture and the cycle double cover conjecture. The text highlights the interrelationships between graph colouring, integer flow, cycle covers and graph minors. It also concentrates on graph theoretical methods and results.