Planar graphs : a historical perspective.

摘要: PLANAR GRAPHS: A HISTORICAL PERSPECTIVE Rick Alan Hudson July 20, 2004 The field of graph theory has been indubitably influenced by the study planar graphs. This thesis, consisting five chapters, is a historical account origins and development concepts pertaining to graphs their applications. first chapter serves as an introduction history theory, including early studies tools such paths, circuits, trees. second pertains relationship between polyhedra graphs, specifically result Euler concerning number vertices, edges, faces polyhedron. Counterexamples generalizations Euler's formula are also discussed. Chapter III describes background in recreational mathematics Ks K3,3 importance characterization Kuratowski. Further characterizations Whitney, Wagner, MacLane addressed. focus IV eventual "proof' four-color theorem, although it includes discussion involving coloring maps on surfaces higher genus. final gives measurements graph's closeness planarity, crossing number, thickness, splitting coarseness. concludes with two other problems Heawood's empire problem Ringel's earth-moon problem.