Издательство Springer, 1996, -142 pp. I started writing this book in 1990 and completed the first draft in October 1991. It then took me another one and a half years (June 1992 to December 1993) to revise the first draft. My objective in writing this book is to give an up-to-date account of total colourings of graphs which can be used as a graph theory course/seminar materials for advanced undergraduate and graduate students and as a reference for researchers. To achieve the objectives, easy-to-read, detailed proofs of almost all of the theorems presented in this book, and numerous examples and exercises are provided here. Many open problems are also mentioned. I hope that through this rapid introduction I shall be able to bring the readers to the frontier of this currently very active field in graph theory. After the first draft of this manuscript was completed, I used it as lecturing material in my graph theory course offered to the advanced undergraduate students of the National University of Singapore (NUS). I thank my students for their patience in attending my lectures and for giving me their valuable feedback. Basic Terminology and Introduction. Some Basic Results. Complete r-Partite Graphs. Graphs of Low Degree. Graphs of High Degree. Classification of Type 1 and Type 2 Graphs. Total Chromatic Number of Planar Graphs. Some Upper Bounds for the Total Chromatic Number of Graphs. Concluding Remarks.
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