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GraphTheory

 ChromaticIndex
 EdgeChromaticNumber

 Calling Sequence ChromaticIndex(G, col) EdgeChromaticNumber(G, col)

Parameters

 G - undirected unweighted graph col - (optional) name

Description

 • ChromaticIndex and EdgeChromaticNumber compute the chromatic index (or edge chromatic number) of a graph G. If a name col is specified, then this name is assigned the list of color classes of an optimal proper edge coloring. The algorithm uses a backtracking technique, except when G is bipartite, where a more efficient algorithm is used.

Examples

 > $\mathrm{with}\left(\mathrm{GraphTheory}\right):$
 > $\mathrm{K4}≔\mathrm{CompleteGraph}\left(4\right)$
 ${\mathrm{K4}}{:=}{\mathrm{Graph 1: an undirected unweighted graph with 4 vertices and 6 edge\left(s\right)}}$ (1)
 > $\mathrm{EdgeChromaticNumber}\left(\mathrm{K4},'\mathrm{col}'\right)$
 ${3}$ (2)
 > $\mathrm{col}$
 $\left[\left\{\left\{{1}{,}{2}\right\}{,}\left\{{3}{,}{4}\right\}\right\}{,}\left\{\left\{{1}{,}{3}\right\}{,}\left\{{2}{,}{4}\right\}\right\}{,}\left\{\left\{{1}{,}{4}\right\}{,}\left\{{2}{,}{3}\right\}\right\}\right]$ (3)
 > $\mathrm{DrawGraph}\left(\mathrm{K4}\right)$