Oxford Lecture Series in Mathematics and its Applications. 11. Oxford: Clarendon Press. 156 p. £27.50 (1998).
“Graph theory as I have known it” is based on a series of lectures that Professor Tutte presented shortly before his retirement from his regular duties at the University of Waterloo in 1984. While this book does not give an in-depth study of all the fundamental topics in graph theory, it does provide a fascinating, well-motivated, clear and concise account of a number of topics to which Professor Tutte made very important contributions. This unique text could serve as an introductory text for graduate students who should benefit from the evolutionary presentation of the material.
The text is divided into twelve chapters. In the opening chapter the author tells how his facination (and that of three of his fellow undergraduate students at Trinity College Cambridge in the 1930s) with a problem in a mathematical puzzles book led to the appearance of graphs as more simplified models in the construction of perfect rectangles. Throughout the remainder of the text, the author indicates how other topics in graph theory evolved from his fruitful collaboration and discussions with these three fellow students at Cambridge. Other topics that are covered include, the development of the authors ideas in disproving Tait’s conjecture for Hamiltonian circuits; his contributions to factors in graphs; extensions of concepts for perfect rectangles and squares to the dissection of parallelograms and triangles; many facets of algebraic graph theory; symmetries of graphs; planarity, planar duality and planar enumeration; graphs and matroids; the reconstruction problem and chromatic polynomials.