Theorems and computations in circular colourings of graphs

The circular chromatic number provides a more refined measure of colourability of graphs, than does the ordinary chromatic number. Thus circular colouring is of substantial importance wherever graph colouring is studied or applied, for example, to scheduling problems of periodic nature. Precisely, the circular chromatic number of a graph G is the smallest ratio p/q of positive integers p and q for which there exists a mapping c:V(G)->{1,2,...,p} such that q