For each minor-closed graph class we show that a simple variant of
Boruvka's algorithm computes a MST for any input graph belonging to
that class with linear costs. Among minor-closed graph classes are
e.g planar graphs, graphs of bounded genus, partial
k-trees for fixed k, and linkless or knotless embedable graphs.
The algorithm can be implemented on a CRCW PRAM to run in
logarithmic time with a work load that is linear in the size of the
graph. We develop a new technique to find multiple edges in such a
graph that might have applications in other parallel reduction
algorithms as well.
