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Topics in Topological Graph Theory by Jonathan L. Gross, Robin J. Wilson, Lowell W. Beineke

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6Colouring graphs on surfaces

JOAN P. HUTCHINSON

1. Introduction

2. High-end colouring

3. A transition from high-end to low-end colouring

4. Colouring graphs with few colours

5. Girth and chromatic number

6. List-colouring graphs

7. More colouring extensions

8. An open problem

References

        This chapter surveys results on embedded graphs whose chromatic numbers are as large as possible (depending on the embedding surface) and as small as possible (depending on graph properties). Results often follow the pattern of precolouring parts of the graph and then extending the precolouring. Many results arise as analogues of planar colouring results, and many have parallels in the newer area of list-colouring.

1. Introduction

While recognizing the ...

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