## Graph theory 1736-1936 |

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1-cells 1-circuits 1-factor adjacent algebra arcs of G atoms Birkhoff boundary branches Cayley chapter chromatic polynomials configuration connected pieces consider construct contains corresponding crossing diagram districts divisions dual equations Euler Euler characteristic Euler's formula Eulerian path example factors figure follows formula four four-colour conjecture four-colour problem G. D. Birkhoff geometry given graph G graph theory Heawood Hence hexagons Icosian Icosian Game irreducible map joined Kirkman knight's tour knots Konigsberg letter Lhuilier lines Math mathematical mathematician matrix meet Mobius neighbouring regions notation nullity number of bridges number of edges number of regions number of vertices obtain odd number one-sided surface paper pentagons Petersen planar graphs plane point of concourse polygons polyhedra polyhedron proof properties proved published reduced regular graph represented result solution sphere subgraph suppose Sylvester symbol Tait theorem topology total number traversed trees triangles trivalent trivalent graph valency vertex Whitney