Decompositions Of Graphs
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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.
Decompositions Of Graphs And Hypergraphs
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Author : Stefan Glock
language : en
Publisher:
Release Date : 2018
Decompositions Of Graphs And Hypergraphs written by Stefan Glock and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
This thesis contains various new results in the areas of design theory and edge decompositions of graphs and hypergraphs. Most notably, we give a new proof of the existence conjecture, dating back to the 19th century. For \(r\)-graphs \(F\) and \(G\), an \(F\)-decomposition of G is a collection of edge-disjoint copies of F in G covering all edges of \(G\). In a recent breakthrough, Keevash proved that every sufficiently large quasirandom \(r\)-graph G has a \(K\)\(_f\)\(^{(r)}\) -decomposition (subject to necessary divisibility conditions), thus proving the existence conjecture. We strengthen Keevash's result in two major directions: Firstly, our main result applies to decompositions into any \(r\)-graph \(F\), which generalises a fundamental theorem of Wilson to hypergraphs. Secondly, our proof framework applies beyond quasirandomness, enabling us e.g. to deduce a minimum degree version. For graphs, we investigate the minimum degree setting further. In particular, we determine the decomposition threshold' of every bipartite graph, and show that the threshold of cliques is equal to its fractional analogue. We also present theorems concerning optimal path and cycle decompositions of quasirandom graphs. This thesis is based on joint work with Daniela Kuhn and Deryk Osthus, Allan Lo and Richard Montgomery.
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 : Marsha Forman Foregger
language : en
Publisher:
Release Date : 1979
Decompositions Of Graphs written by Marsha Forman Foregger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Graph theory categories.
Neighbour Distinguishing Decompositions Of Graphs
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Author : Mohammed Senhaji
language : en
Publisher:
Release Date : 2018
Neighbour Distinguishing Decompositions Of Graphs written by Mohammed Senhaji and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
In this thesis we explore graph decompositions under different constraints. The title of the is due to the fact that most of these decompositions are neighbour-distinguishing. That is, we can extract from each such decomposition a proper vertex colouring. Moreover, most of the considered decompositions are edge partitions, and therefore can be seen as edge-colourings. The main question presented in this thesis is was introduced by Karoński, Łuczak and Thomason in [KLT04]: Can we weight the edges of a graph G, with weights 1, 2, and 3, such that any two of adjacent vertices of G are distinguished by the sum of their incident weights ? This question later becomes the famous 1-2-3 Conjecture. In this thesis we explore several variants of the 1-2-3 Conjecture, and their links with locally irregular decompositions. We are interested in both optimisation results and algorithmic problems. We first introduce an equitable version of the neighbour-sum- distinguishing edge-weightings, that is a variant where we require every edge weight to be used the same number of times up to a difference of 1. Then we explore an inject- ive variant where each edge is assigned a different weight, which yields necessarily an equitable weighting. This gives us first general upper bounds on the equitable version. Moreover, the injective variant is also a local version of the well-known antimagic la- belling. After that we explore how neighbour-sum-distinguishing weightings behave if we require sums of neighbouring vertices to differ by at least 2. Namely, we present results on the smallest maximal weight needed to construct such weightings for some classes of graphs, and study some algorithmic aspects of this problem. Due to the links between neighbour-sum-distinguishing edge weightings and locally irregular decompositions, we also explore the locally irregular index of subcubic graphs, along with other variants of the locally irregular decomposition problem. Finally, we present a more general work to- ward a general theory unifying nsd edge-weightings and locally irregular decompositions. We also present a 2-player game version of neighbour-sum-distinguishing edge-weightings and exhibit sufficient conditions for each player to win the game.
Transitive Decompositions Of Graphs
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Author : Geoffrey Pearce
language : en
Publisher:
Release Date : 2007
Transitive Decompositions Of Graphs written by Geoffrey Pearce and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Decomposition (Mathematics) categories.
A transitive decomposition of a graph is a partition of the arc set such that there exists a group of automorphisms of the graph which preserves and acts transitively on the partition. This turns out to be a very broad idea, with several striking connections with other areas of mathematics. In this thesis we first develop some general theory of transitive decompositions, and in particular we illustrate some of the more interesting connections with certain combinatorial and geometric structures. We then give complete, or nearly complete, structural characterisations of certain classes of transitive decompositions preserved by a group with a rank 3 action on vertices (such a group has exactly two orbits on ordered pairs of distinct vertices). The main classes of rank 3 groups we study (namely those which are imprimitive, or primitive of grid type) are derived in some way from 2-transitive groups (that is, groups which are transitive on ordered pairs of distinct vertices), and the results we achieve make use of the classification by Sibley in 2004 of transitive decompositions preserved by a 2-transitive group.
On Isomorphic Decompositions Of Graphs
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Author : Sergio Ruiz
language : en
Publisher:
Release Date : 1983
On Isomorphic Decompositions Of Graphs written by Sergio Ruiz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Graph theory categories.
On Eulerian Irregularity And Decompositions In Graphs
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Author : Eric Andrews
language : en
Publisher:
Release Date : 2014
On Eulerian Irregularity And Decompositions In Graphs written by Eric Andrews 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.
Abstract is available as a pdf file. http://scholarworks.wmich.edu/cgi/viewcontent.cgi?filename=0&article=1271&context=dissertations&type=additional
Vertex Decompositions Of Graphs
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Author : David Howard Rees
language : en
Publisher:
Release Date : 1979
Vertex Decompositions Of Graphs written by David Howard Rees and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with categories.