1. Oaths 2. Circuits 3. Trees 4. Chemical graphs 5. Euler's polyhedral formula 6. The four-colour problem - early history 7. Colouring maps on surfaces 8. Ideas from algebra and topology 9. The four-colour problem - to 1936 10. The factorization of graphs Appendix 1: Graph theory since 1936 Appendix 2: Bibliographical notes Appendix 3: Bibliography: 1736-1936

A (3, 4)-biregular bigraph G is a bipartite graph where all vertices in one part have degree 3 and all vertices in the other part have degree 4. A path factor of G is a spanning subgraph whose… Expand

Ancient Greek mathematicians tried to establish their theory of area and volume by means of “geometric algebra”. Namely, in order to compare the area (or volume) of two figures, they made up an… Expand

In this thesis, we use computer methods to investigate Hamilton cycles and paths in several families of graphs where general results are incomplete, including Kneser graphs, cubic Cayley graphs and… Expand

PLANAR GRAPHS: A HISTORICAL PERSPECTIVE Rick Alan Hudson July 20, 2004 The field of graph theory has been indubitably influenced by the study of planar graphs. This thesis, consisting of five… Expand

This dissertation explores and advances results for several variants on a longopen problem in graph coloring. Steinberg’s conjecture states that any planar graph containing no 4-cycles or 5-cycles is… Expand