“The book gives a detailed survey on concepts of vertex-colorings which are induced by edge-colorings. … It is well written and provides a good introduction and survey on color-induced graph colorings for researchers and graduate students in the mathematics community, especially the graph theory community.” (Eckhard Steffen, zbMATH, Vol. 1365.05006, 2017)

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.
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A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. This gives rise to a discussion of irregular colorings, strong colorings, modular colorings, edge-graceful colorings, twin edge colorings and binomial colorings.
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1. Introduction.- 2. The Irregularity Strength of a Graph.- 3. Modular Sum-Defined Irregular Colorings.- 4. Set-Defined Irregular Colorings.- 5. Multiset-Defined Irregular Colorings.- 6. Sum-Defined Neighbor-Distinguishing Colorings.- 7. Modular Sum-Defined Neighbor-Distinguishing Colorings.- 8. Strong Edge Colorings of Graphs.- 9. Sum-Defined Chromatic Indices.- References.- Index.
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Provides intriguing open problems and conjectures Offers a comprehensive treatment of numerous color-induced graph colorings Presents the background and motivation for the concept of color-induced colorings of graphs Includes supplementary material: sn.pub/extras
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GPSR Compliance The European Union's (EU) General Product Safety Regulation (GPSR) is a set of rules that requires consumer products to be safe and our obligations to ensure this. If you have any concerns about our products you can contact us on ProductSafety@springernature.com. In case Publisher is established outside the EU, the EU authorized representative is: Springer Nature Customer Service Center GmbH Europaplatz 3 69115 Heidelberg, Germany ProductSafety@springernature.com
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Produktdetaljer

ISBN
9783319203935
Publisert
2015-08-18
Utgiver
Vendor
Springer International Publishing AG
Høyde
235 mm
Bredde
155 mm
Aldersnivå
Research, P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet

Forfatter