Color-Induced Graph Colorings

Ping Zhang (Autor)

Buch | Softcover

XIV, 118 Seiten

2015 | 1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-20393-5 (ISBN)

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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.

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.

"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)

Erscheint lt. Verlag	18.8.2015
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	XIV, 118 p. 48 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
Schlagworte	colored-induced • combinatorics • Graph colorings • Monochromatic Vertex Colorings • neighbor-distinguishing • Proper Vertex Colorings • Rainbow Vertex Colorings
ISBN-10	3-319-20393-2 / 3319203932
ISBN-13	978-3-319-20393-5 / 9783319203935
Zustand	Neuware