  A graph $G$ is nonseparating projective planar if $G$ has a projective planar
embedding without a nonsplit link. Nonseparating projective planar graphs are
closed under taking minors and are a superclass of projective outerplanar
graphs. We partially characterize the minor-minimal separating projective
planar graphs by proving that given a minor-minimal nonouter-projective-planar
graph $G$, either $G$ is minor-minimal separating projective planar or $G
\dot\cup K_{1}$ is minor-minimal weakly separating projective planar, a
necessary condition for $G$ to be separating projective planar.
  One way to generalize separating projective planar graphs is to consider type
I 3-links consisting of two cycles and a pair of vertices. A graph is
intrinsically projective planar type I 3-linked (IPPI3L) if its every
projective planar embedding contains a nonsplit type I 3-link. We partially
characterize minor-minimal IPPI3L graphs by classifying all minor-minimal
IPPI3L graphs with three or more components, and finding many others with fewer
components.
