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Is there a recursive formulae to compute the edge chromatic polynomial of a graph? The following formulae is known for the vertex chromatic polynomial of a grapg $G$ $P(G,x)=P(G-uv, x)- P(G/uv,x)$ (See https://en.wikipedia.org/wiki/Chromatic_polynomial)

Note that by the formulae I do not mean using the above formuale for the line graph of the graph.

Actually I would like to compute the edge chromatic polynomial of all graphs with seven vertices and I could not compute some of them by MAPLE.

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    $\begingroup$ It really feels like any reasonable recursion will be more or less isomorphic to doing the classical formula on the line graph. $\endgroup$
    – Per Alexandersson
    Commented Sep 16, 2015 at 21:32

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