Universal point sets for planar graphs ★★★
Author(s): Mohar
We say that a set is -universal if every vertex planar graph can be drawn in the plane so that each vertex maps to a distinct point in , and all edges are (non-intersecting) straight line segments.
Question Does there exist an -universal set of size ?
Keywords: geometric graph; planar graph; universal set
Antichains in the cycle continuous order ★★
Author(s): DeVos
If , are graphs, a function is called cycle-continuous if the pre-image of every element of the (binary) cycle space of is a member of the cycle space of .
Problem Does there exist an infinite set of graphs so that there is no cycle continuous mapping between and whenever ?
Drawing disconnected graphs on surfaces ★★
Author(s): DeVos; Mohar; Samal
Conjecture Let be the disjoint union of the graphs and and let be a surface. Is it true that every optimal drawing of on has the property that and are disjoint?
Keywords: crossing number; surface