Optimal edge-colourings for a class of planar multigraphs (Q5955208)

The author determines the chromatic index of multigraphs containing no minors isomorphic either to \(K_{3,3}\) or \({K_5}-e\) (this latter means \(K_5\) without one of its edges). The answer (the maximum of the maximum valency and a function on the odd subset of the vertices) partially verifies a conjecture of \textit{P. D. Seymour} [J. Comb. Theory, Ser. B 31, 82--94 (1981; Zbl 0471.05031)] and is a generalization of a result of \textit{P. D. Seymour} [Combinatorica 10, No. 4, 379--392 (1990; Zbl 0721.05023)] for series-parallel graphs.