Courcelle

Beyond Outerplanarity

Announce Type: replace Abstract: We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., \emph{convex drawings}. We consider two families of graph classes with convex drawings: \emph{outer $k$-planar} graphs, where each edge is crossed by at most $k$ other edges; and \emph{outer $k$-quasi-planar} graphs, where no $k$ edges can mutually cross. We show that the outer $k$-planar graphs are $\lfloor3.5\sqrt{k}\rfloor$-degenerate, and...