Graph Theory. 1736-1936

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  • Pages : XI-239
  • Nombre de volumes : 1
  • Support : Document imprimé
  • Format : 23 cm.
  • Langues : Anglais
  • Édition : Original
  • Ville : Oxford
  • ISBN : 0-19-853901-0
  • Date de création : 07-02-2011
  • Dernière mise à jour : 11-11-2011



Mathematicians have often pursued their researches in an erratic and intuitive way, rather than by the clear light of logic. Consequently, the historical development of the subject frequently differs considerably from the systematic approach which one finds in most textbooks. This book follows an historical approach, and gives a self-contained introduction to the subject of graph theory. – The central feature is a set of 37 extracts taken from the original writings of mathematicians who contributed to the foundations of graph theory. The book has ten chapters, each one dealing with a particular theme in graph theory, and containing three or four main extracts. – 1. Paths (The problem of the Königsberg bridges; Diagram-tracing puzzles; Mazes and labyrinths); – 2. Circuits (The knight's tour; Kirkman and polyhedra; The Icosian Game); – 3. Trees (The first studies of trees; Counting unrooted trees; Counting labelled trees); – 4. Chemical graphs (Graphic formulae in chemistry; Isomerism; Clifford, Sylvester, and the term “graph”; Enumeration, from Caylay to Polya); – 5. Euler's polyhedral formula (The history of polyhedra; Planar graphs and maps; Generalizations of Euler's formula); – 6. The four-colour problem. Early history (The origin of the four-colour problem; The “proof”; Heawood and the five-colour theorem); – 7. Colouring maps on surfaces (The chromatic number of a surface; Neighbouring regions; One-sided surfaces); – 8. Ideas from algebra and topology (The algebra of circuits; Planar graphs; Planarity and Whitney duality); – 9. The four-colour problem : to 1936 (The first attempts to reformulate the problem; Reducibility; Birkhoff, Whitney, and chromatic polynomials); – 10. The factorization of graphs (Regular graphs and their factors; Petersen's theorem on trivalent graphs; An alternative view : correspondences). – Appendix 1 : Graph theory since 1936; – Appendix 2 : Biographical notes; – Appendix 3 : Bibliography. 1736-1936.