## Graph Theory, 1736-1936First published in 1976, this book has been widely acclaimed both for its significant contribution to the history of mathematics and for the way that it brings the subject alive. Building on a set of original writings from some of the founders of graph theory, the book traces the historical development of the subject through a linking commentary. The relevant underlying mathematics is also explained, providing an original introduction to the subject for students. From reviews: 'The book...serves as an excellent examplein fact, as a modelof a new approach to one aspect of mathematics, when mathematics is considered as a living, vital and developing tradition.' (Edward A. Maziark in Isis) 'Biggs, Lloyd and Wilson's unusual and remarkable book traces the evolution and development of graph theory...Conceived in a very original manner and obviously written with devotion and a very great amount of painstaking historical research, it contains an exceptionally fine collection of source material, and to a graph theorist it is a treasure chest of fascinating historical information and curiosities with rich food for thought.'(Gabriel Dirac in Centaurus) 'The lucidity, grace and wit of the writing makes this book a pleasure to read and re-read.' (S. H. Hollingdale in Bulletin of the Institute of Mathematics and its Applications) |

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This book gives a self contained historical introduction to graph theory using thirty-seven extracts from original articles (translated when necessary).

### Contents

PATHS | 3 |

CIRCUITs | 21 |

tr | 37 |

CHEMICAL GRAPHS | 55 |

EULERs POLY HEDRAL FORMULA | 74 |

The FOURCOLOUR PROBLEM | 90 |

COLOURING MAPS ON SURFACES | 109 |

Neighbouring regions | 115 |

Onesided surfaces | 124 |

THE FOURCOLOUR PROBLEMTO 1936 | 158 |

THE FACTORIZATION OF GRAPHS | 187 |

Graph Theory since 1936 | 209 |

225 | |

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### Common terms and phrases

1-cells 1-circuits 1-factor adjacent algehra Amer areas atoms Birkhoff Cayley chapter chromatic polynomials circuit configuration connected pieces construct contains corresponding denote descrihe diagram districts divisions dual equations Euler Euler's formula Eulerian path example faces factors figure follows formula four four-colour conjecture four-colour problem geometry given graph G graph theory Graphen Heawood heen Hence hetween hexagons hlue hoth houndary hranches hridges joined Kempe Kirkman knight's tour knots Kuratowski Kuratowski's theorem lahels letter Lhuilier lines mathematical mathematician matrix Möbius Möbius strip neighbouring regions notation nullity number of bridges number of vertices numher of edges obtain one-sided surface paper pentagons Petersen planar graphs plane point of concourse polygons polyhedra polyhedron possihle proof properties proved puhlished regular graph represented result solution sphere subgraph suppose Sylvester symbol theorem topology total numher traversed trees triangles trivalent trivalent graph valency vertex Whitney