N. Y. ; L. : Academic Press, 1967.— xvi, 260 p.
Puzzling problems permeate mathematics, and this is probably the strongest reason for the burgeoning growth of this queen of the sciences. The object of this book is to discuss the methods in graph theory that have been developed in the last century for attacking the four-color problem. It may be said without exaggeration conceing the writers on graph theory in this period, that however practical were the problems they examined, or however abstract their papers may appear to be, the author nearly always seems to have had some thoughts in mind regarding their application to the four-color problem.
The literature on the subject is voluminous and widely scattered. This book gives the first comprehensive analysis of this material and a discussion of the results that exist. All proofs and presentations have been examined and in many cases extensively revised. It has been the author’s intention to take into account all important related studies in graph theory. No proof of the four-color problem is included, of course. But, as one often sees in the history of mathematics, a fresh and comprehensive review of a subject has been the starting point for strong progress by the younger generation of mathematicians.
A book on the four-color problem must lean heavily on general graph theory, and various aspects of graphs had to be developed as an adjunct to our discussions.
Pure and Applied Mathematics (A Series of Monographs and Textbooks), Vol. 27
Planar Graphs.
Bridges and Circuits.
Dual Graphs.
Euler’s Formula and Its Consequences.
Large Circuits.
Colorations.
Color Functions.
Formulations of the Four-Color Problem.
Cubic Graphs.
Hadwiger’s Conjecture.
Critical Graphs.
Planar 5-Chromatic Graphs.
Three Colors.
Edge Coloration.
Puzzling problems permeate mathematics, and this is probably the strongest reason for the burgeoning growth of this queen of the sciences. The object of this book is to discuss the methods in graph theory that have been developed in the last century for attacking the four-color problem. It may be said without exaggeration conceing the writers on graph theory in this period, that however practical were the problems they examined, or however abstract their papers may appear to be, the author nearly always seems to have had some thoughts in mind regarding their application to the four-color problem.
The literature on the subject is voluminous and widely scattered. This book gives the first comprehensive analysis of this material and a discussion of the results that exist. All proofs and presentations have been examined and in many cases extensively revised. It has been the author’s intention to take into account all important related studies in graph theory. No proof of the four-color problem is included, of course. But, as one often sees in the history of mathematics, a fresh and comprehensive review of a subject has been the starting point for strong progress by the younger generation of mathematicians.
A book on the four-color problem must lean heavily on general graph theory, and various aspects of graphs had to be developed as an adjunct to our discussions.
Pure and Applied Mathematics (A Series of Monographs and Textbooks), Vol. 27
Planar Graphs.
Bridges and Circuits.
Dual Graphs.
Euler’s Formula and Its Consequences.
Large Circuits.
Colorations.
Color Functions.
Formulations of the Four-Color Problem.
Cubic Graphs.
Hadwiger’s Conjecture.
Critical Graphs.
Planar 5-Chromatic Graphs.
Three Colors.
Edge Coloration.