We study biplane graphs drawn on a finite planar point set \(S\) in general position. This is the family of geometric graphs whose vertex set is \(S\) and can be decomposed into two plane graphs. We show that two maximal biplane graphs—in the sense th . . .

It is shown that every disconnected vertex-colored plane straight line graph with no isolated vertices can be augmented (by adding edges) into a connected plane straight line graph such that the new edges respect the coloring and the degree of every v . . .

We study biplane graphs drawn on a finite point set S in the plane in general position. This is the family of geometric graphs whose vertex set is S and which can be decomposed into two plane graphs. We show that every sufficiently large point set adm . . .