It is shown here that for every fixed k, Bk-VPG $\subsetneq$Bk+1- VPG is in no inclusion relation with the class of intersection graphs of straight line segments in the plane.Expand

A comprehensive study of classes of graphs between grid intersection graphs and bipartite permutation graphs and the containment relation on these classes is provided.Expand

A polynomial-time algorithm for partial representation extension of circle graphs that describes the structure of all representation a circle graph based on split decomposition and shows whether one can draw the remaining chords into a partially pre-drawn representation.Expand

This paper disproves the conjecture that all planar graphs are B3-VPG, and shows that the 4-connected planar graph constitute a subclass of the intersection graphs of Z-shapes, and demonstrates that a B2-V PG representation of a planargraph can be constructed in O(n) time.Expand

These are the first classes of geometric graphs where extending partial representations is provably harder than recognition, as opposed to e.g. interval graphs, circle graphs, permutation graphs or even standard representations of plane graphs.Expand

This work investigates the problem of drawing graphs in 2D and 3D such that their edges (or only their vertices) can be covered by few lines or planes, and shows lower and upper bounds for the numbers of lines and planes needed for covering drawings of graphs in certain graph classes.Expand