✦ LIBER ✦

Total Colourings of Graphs

✍ Scribed by Hian-Poh Yap (auth.)

Book ID: 127406510
Publisher: Springer
Year: 1996
Tongue: English
Weight: 830 KB
Edition: 1
Category: Library
City: Berlin; New York
ISBN: 3540493018
DOI: 10.1007/BFb0092895

No coin nor oath required. For personal study only.

✦ Synopsis

This book provides an up-to-date and rapid introduction to an important and currently active topic in graph theory. The author leads the reader to the forefront of research in this area. Complete and easily readable proofs of all the main theorems, together with numerous examples, exercises and open problems are given. The book is suitable for use as a textbook or as seminar material for advanced undergraduate and graduate students. The references are comprehensive and so it will also be useful for researchers as a handbook.

✦ Subjects

Combinatorics

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It is proved that if G is a planar graph with total (vertex-edge) chromatic number χ , maximum degree and girth g, then χ = + 1 if ≥ 5 and g ≥ 5, or ≥ 4 and g ≥ 6, or ≥ 3 and g ≥ 10. These results hold also for graphs in the projective plane, torus and Klein bottle.

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We give a new upper bound on the total chromatic number of a graph. This bound improves the results known for some classes of graphs. The bound is stated as follows: ZT ~< Z~ + L l3 ~ J + 2, where Z is the chromatic number, Z~ is the edge chromatic number (chromatic index) and ZT is the total chroma

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