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The CircularChromaticIndex and CircularEdgeChromaticNumber commands return the circular chromatic index (circular edge 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 edge coloring. The algorithm uses a backtracking technique.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$P≔\mathrm{PetersenGraph}\left(\right)$

$P≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 15\; edges}$

$\mathrm{CircularChromaticIndex}\left(P\,'\mathrm{col}'\right)$

$\frac{11}{3}$

$\mathrm{col}$

$\left[\left\{1\,2\right\}=0\,\left\{1\,5\right\}=3\,\left\{1\,6\right\}=6\,\left\{2\,3\right\}=3\,\left\{2\,9\right\}=8\,\left\{3\,4\right\}=6\,\left\{3\,7\right\}=9\,\left\{4\,5\right\}=10\,\left\{4\,10\right\}=2\,\left\{5\,8\right\}=7\,\left\{6\,7\right\}=1\,\left\{6\,10\right\}=9\,\left\{7\,8\right\}=4\,\left\{8\,9\right\}=0\,\left\{9\,10\right\}=5\right]$