For forbidden families of odd cycles and cliques, the edge-coloring problem with forbidden patterns is poly-time equivalent to its precolored version and to a finite CSP, yielding a P versus NP-complete dichotomy.
The R amsey property for graphs with forbidden complete subgraphs
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Edge-coloring problems with forbidden patterns and planted colors
For forbidden families of odd cycles and cliques, the edge-coloring problem with forbidden patterns is poly-time equivalent to its precolored version and to a finite CSP, yielding a P versus NP-complete dichotomy.