## Exploring graph theory, Volume 2 |

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1-factor 3-colouring 6raphs adjacent vertices aesh algorithm aore Assuae aust bipartite graph boundary bridges chromatic nuaber chromatic polynomial complete graph component contains contradiction corresponding crossing nuabers crossing points cut-set cut-vertex deiinition deleting diagonal drawing drawn dual edge-disjoint edges incident edges joining Euler's theorem Eulerian circuit Eulerian graph Eulerian path Exaaples exterior region extra edge F regions four colour four colour theorem froa graph isomorphic graph of fig graph theory Hamiltonian circuit Hamiltonian graphs hexomino homeomorphic iaplies including the exterior induction integer Katheiatical least non-planar graph nuaber of edges nuaber of regions nuaber of vertices nuabers assigned odd degree pair parallel edges path Petersen graph planar graph polygon problem Prooi properly coloured prove randomly Eulerian resulting graph saae colour satisfies conditions Schlegel diagraa second colour set of edges six vertices spanning tree subgraph Suppose vertices adjacent vertices coloured vertices of degree vertices of odd