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GraphTheory

 CircularChromaticNumber

 Calling Sequence CircularChromaticNumber(G, col)

Parameters

 G - undirected unweighted graph col - (optional) name

Description

 • The CircularChromaticNumber command returns the circular chromatic number of a graph G. If a name col is specified, then this name is assigned the list of colors of an optimal proper coloring of vertices. The algorithm uses a backtracking technique.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{with}\left(\mathrm{SpecialGraphs}\right):$
 > $G≔\mathrm{FlowerSnark}\left(5\right):$
 > $\mathrm{CircularChromaticNumber}\left(G,'\mathrm{col}'\right)$
 $\frac{{5}}{{2}}$ (1)
 > $\mathrm{col}$
 $\left[{0}{,}{2}{,}{4}{,}{1}{,}{3}{,}{2}{,}{0}{,}{2}{,}{0}{,}{2}{,}{4}{,}{1}{,}{4}{,}{1}{,}{3}{,}{1}{,}{3}{,}{0}{,}{3}{,}{0}\right]$ (2)