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revised Number of simple edge-disjoint paths needed to cover a planar graph
more precise lower bound
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comment Number of simple edge-disjoint paths needed to cover a planar graph
@EinarRødland: I oversimplified and made an estimation with $3|V|$ edges instead of $3|V|-6$ edges. If you use the later bound you get $m/6 + 1$ paths (as for the icosahedron or tetrahedron). Still my main question is, whether the degree constraint is the only constraint for a path cover.
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fixed interpretation
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comment Complete graph invariant
cross-posted: cs.stackexchange.com/questions/14147/complete-graph-invariant
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comment Origin of the term “planar graph”
Thanks for the pointer. This is a cool book. It helped me a bit further (see additional remarks in the question), but I do not a have a definite answer yet.