Color-Induced Graph Colorings - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Color-Induced Graph Colorings write by Ping Zhang. This book was released on 2015-08-10. Color-Induced Graph Colorings available in PDF, EPUB and Kindle. A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. The coloring concepts described in this book depend not only on the property required of the initial edge coloring and the kind of objects serving as colors, but also on the property demanded of the vertex coloring produced. For each edge coloring introduced, background for the concept is provided, followed by a presentation of results and open questions dealing with this topic. While the edge colorings discussed can be either proper or unrestricted, the resulting vertex colorings are either proper colorings or rainbow colorings. This gives rise to a discussion of irregular colorings, strong colorings, modular colorings, edge-graceful colorings, twin edge colorings and binomial colorings. Since many of the concepts described in this book are relatively recent, the audience for this book is primarily mathematicians interested in learning some new areas of graph colorings as well as researchers and graduate students in the mathematics community, especially the graph theory community.
Graph Coloring Problems
Graph Coloring Problems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Graph Coloring Problems write by Tommy R. Jensen. This book was released on 2011-10-24. Graph Coloring Problems available in PDF, EPUB and Kindle. Contains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature. The book will stimulate research and help avoid efforts on solving already settled problems. Each chapter concludes with a comprehensive list of references which will lead readers to original sources, important contributions and other surveys.
Handbook of Combinatorial Optimization
Handbook of Combinatorial Optimization - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Handbook of Combinatorial Optimization write by Ding-Zhu Du. This book was released on 2006-08-18. Handbook of Combinatorial Optimization available in PDF, EPUB and Kindle. This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.
Distributed Graph Coloring
Distributed Graph Coloring - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Distributed Graph Coloring write by Leonid Barenboim. This book was released on 2022-06-01. Distributed Graph Coloring available in PDF, EPUB and Kindle. The focus of this monograph is on symmetry breaking problems in the message-passing model of distributed computing. In this model a communication network is represented by a n-vertex graph G = (V,E), whose vertices host autonomous processors. The processors communicate over the edges of G in discrete rounds. The goal is to devise algorithms that use as few rounds as possible. A typical symmetry-breaking problem is the problem of graph coloring. Denote by ? the maximum degree of G. While coloring G with ? + 1 colors is trivial in the centralized setting, the problem becomes much more challenging in the distributed one. One can also compromise on the number of colors, if this allows for more efficient algorithms. Other typical symmetry-breaking problems are the problems of computing a maximal independent set (MIS) and a maximal matching (MM). The study of these problems dates back to the very early days of distributed computing. The founding fathers of distributed computing laid firm foundations for the area of distributed symmetry breaking already in the eighties. In particular, they showed that all these problems can be solved in randomized logarithmic time. Also, Linial showed that an O(?2)-coloring can be solved very efficiently deterministically. However, fundamental questions were left open for decades. In particular, it is not known if the MIS or the (? + 1)-coloring can be solved in deterministic polylogarithmic time. Moreover, until recently it was not known if in deterministic polylogarithmic time one can color a graph with significantly fewer than ?2 colors. Additionally, it was open (and still open to some extent) if one can have sublogarithmic randomized algorithms for the symmetry breaking problems. Recently, significant progress was achieved in the study of these questions. More efficient deterministic and randomized (? + 1)-coloring algorithms were achieved. Deterministic ?1 + o(1)-coloring algorithms with polylogarithmic running time were devised. Improved (and often sublogarithmic-time) randomized algorithms were devised. Drastically improved lower bounds were given. Wide families of graphs in which these problems are solvable much faster than on general graphs were identified. The objective of our monograph is to cover most of these developments, and as a result to provide a treatise on theoretical foundations of distributed symmetry breaking in the message-passing model. We hope that our monograph will stimulate further progress in this exciting area.
Distributed Graph Coloring
Distributed Graph Coloring - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Distributed Graph Coloring write by Leonid Barenboim. This book was released on 2013-07-01. Distributed Graph Coloring available in PDF, EPUB and Kindle. The objective of our monograph is to cover the developments on the theoretical foundations of distributed symmetry breaking in the message-passing model. We hope that our monograph will stimulate further progress in this exciting area.
