  We show that every $n$-vertex planar graph admits a simultaneous embedding
with no mapping and with fixed edges with any $(n/2)$-vertex planar graph. In
order to achieve this result, we prove that every $n$-vertex plane graph has an
induced outerplane subgraph containing at least $n/2$ vertices. Also, we show
that every $n$-vertex planar graph and every $n$-vertex planar partial 3-tree
admit a simultaneous embedding with no mapping and with fixed edges.
