Graphs whose circular chromatic number equals the chromatic number
The circular chromatic number of a graph is the infimum (in fact, the minimum) of \({k}/{d}\) where there is a coloring \(f\) of the vertices with colors \(1,2,\dots,k\) in such a way that \(d\leq | f(x)-f(y)| \leq k-d\) holds when \(x\), \(y\) are adjacent. Based on the notion of \(n\)-circular superedge, construtions are given for graphs with the chromatic number being equal to the circular chromatic number in the style of Hajós' method for constructing all \(n\)-chromatic graphs. This way, several new planar graphs are constructed, thus settling some earlier problems.
scientific article; zbMATH DE number 1376201