Answer to Question #190876 in Discrete Mathematics for Ali

Question

Let n be 26. Construct a map of a continent having n different countries in such a way that four colours are needed to colour bordering countries in different colours. Using blue for the ocean (and possibly for some of the countries), and three other colours of your choice for the countries, apply colours to the map. [Use four colours whose names start with different letters, so that you can represent each colour with the first letter of its name.]

(b) By inserting vertices at strategic locations, convert your map into a connected planar graph in which faces separated by an edge are differently coloured.

(c) Construct the dual graph of your connected planar graph, and apply the corresponding vertex colouring to your dual graph

please i need answer in simple form with clear explanation to understand , i need answer as requirement

Answer 1

Map of 26 countries with boundary .

(b)

This is a connected Planner graph in which faces separated by and edge are different colored.

(c)

This is the dual graph of the connected planer graph.