Edge coloring planar graphs with two outerplanar subgraphs

The standard problem of edge coloring a graph with k colors is equivalent to partitioning the edge set of the graph into k matchings. Here edge coloring is generalized by replacing matchings with outerplanar graphs. We give a polynomial-time algorithm that edge colors any planar graph with two outerplanar subgraphs. Two is clearly minimal for the class of planar graphs.

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