(University of Oregon, 1988-04-06) Lingas, Andrzej; Proskurowski, Andrzej
We consider the problems of subgraph homeomorphism with fixed pattern graph,
recognition, and subgraph isomorphism for some classes of planar graphs. Following
the results of Robertson and Seymour on forbidden minor characterization, we show
that the problems of fixed subgraph homeomorphism and recognition for any family
of planar graphs closed under minor taking are in NC (i.e., they can be solved by an
algorithm running in poly-log time using polynomial number of processors). We also
show that the related subgraph isomorphism problem for biconnected outerplanar
·graphs is in NC. This is the first example of a restriction of subgraph isomorphism
to a non-trivial graph family admitting an NC algorithm
