Cycles In Graphs
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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.
Cycles In Graphs
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Author : B.R. Alspach
language : en
Publisher: Elsevier
Release Date : 1985-08-01
Cycles In Graphs written by B.R. Alspach and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-08-01 with Mathematics categories.
This volume deals with a variety of problems involving cycles in graphs and circuits in digraphs. Leading researchers in this area present here 3 survey papers and 42 papers containing new results. There is also a collection of unsolved problems.
Cycles And Rays
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Author : Gena Hahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
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 2012-12-06 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.
On Longest Cycles In Graphs
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Author : Deying Li
language : en
Publisher:
Release Date : 1998
On Longest Cycles In Graphs written by Deying Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Paths and cycles (Graph theory) categories.
Abstract: "Dirac proved that every 2-connected graph of order n and minimum degree k admits a cycle of length at least min[n, 2k]. As a possible improvement, Woodall conjectured that if a 2-connected graph of order n has at least n/2 + k vertices of degree at least k, then it has a cycle of length at least 2k. Häggkvist and Jackson showed that this conjecture is true if n [
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.
Even Cycles In Graphs With Many Odd Cycles
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Author : Ralph J. Faudree
language : en
Publisher:
Release Date : 1998
Even Cycles In Graphs With Many Odd Cycles written by Ralph J. Faudree and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Graph theory categories.
Abstract: "It will be shown that if G is a graph of order n containing a triangle, a cycle of length n or n-1 and at least cn odd cycles of different lengths for some positive constant c, then there exists some positive constant k such that G contains at least kn[superscript 1/6] even cycles of different lengths. Other results on the number of even cycle lengths implied by odd cycle lengths will be given."
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.
Interchangeability Of Relevant Cycles In Graphs
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Author :
language : en
Publisher:
Release Date : 1999
Interchangeability Of Relevant Cycles In Graphs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
The set R of relevant cycles of a graph G is the union of its minimum cycle bases. We introduce a partition of R such that each cycle in a class W can be expressed as a sum of other cycles in W and shorter cycles. It is shown that each minimum cycle basis contains the same number of representatives of a given class W. This result is used to derive upper and lower bounds on the number of distinct minimum cycle bases. Finally, we give a polynomial-time algorithm to compute this partition. (author's abstract).
Cycles In Graphs
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Author : B. Jackson
language : en
Publisher:
Release Date : 1978
Cycles In Graphs written by B. Jackson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.
On Cycles In Graphs
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Author : Sheng Bau
language : en
Publisher:
Release Date : 1989
On Cycles In Graphs written by Sheng Bau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Graph theory categories.