the map-colourer and the travelling salesman

The map-colourer's new client wanted a map in which the same colour was not to be used for any two adjacent regions sharing a common border. The map colourer's problem was that he only had four colours, and he didn't want to start colouring in and then find he needed more colours to satisfy the client's request. So he called the travelling salesman who was the only source of coloured pencils in