B-sets and planar maps

Semi-θ-Open Sets and New Classes of Maps

Planar Maps and Airy Phenomena

Fitting Planar Graphs on Planar Maps

Graph and cartographic visualization have the common objective to provide intuitive understanding of some underlying data. We consider a problem that combines aspects of both by studying the problem of fitting planar graphs on planar maps. After providing an NP-hardness result for the general decision problem, we identify sufficient conditions so that a fit is possible on a map with rectangular...

Planar Linkages and Algebraic Sets

An abstract linkage is a one dimensional simplicial complex L with a positive number `(vw) assigned to each edge vw. A planar realization of an abstract linkage (L, `) is a mapping φ from the vertices of L to C so that |φ(v) − φ(w)| = `(vw) for all edges vw. We will investigate the topology of the space of planar realizations of linkages. You may think of an abstract linkage as an ideal mechani...

Gray coding planar maps

The idea of (combinatorial) Gray codes is to list objects in question in such a way that two successive objects differ in some pre-specified small way. In this paper, we utilize β-description trees to cyclicly Gray code three classes of cubic planar maps, namely, bicubic planar maps, 3-connected cubic planar maps, and cubic non-separable planar maps.