Abstract
Let G be a bipartite graph, and let ‚e;‚i be two parallel convex curves; we study the question about whether G admits a planar straight-line drawing such that the vertices of one partite set of G lie on ‚e and the vertices of the other partite set lie on ‚i. A characterization is presented that gives rise to linear time testing algorithm. We also describe a drawing algorithm that runs in linear time if the curves are two concentric circles and the real RAM model of computation is adopted.
Highlights
Common requirements for drawing a bipartite graph are that the bipartition is highlighted in the visualization by representing the vertices on two distinct layers, the edges have as few bends as possible, and the number of edge crossings is minimized
A bipartite graph is a biplanar graph if it has a straight-line crossing-free drawing where the vertices of one partite set are on a horizontal layer and the vertices of the other partite set are on a separate parallel horizontal layer [6]
This paper studies planar drawings of bipartite graphs where vertices are constrained to be on two parallel convex curves, which generalizes the case of horizontal layers
Summary
Common requirements for drawing a bipartite graph are that the bipartition is highlighted in the visualization by representing the vertices on two distinct layers, the edges have as few bends as possible, and the number of edge crossings is minimized. This paper studies planar drawings of bipartite graphs where vertices are constrained to be on two parallel convex curves, which generalizes the case of horizontal layers. Let G be a bipartite graph, and let λe, λi be two parallel convex curves; we want to answer the question about whether G admits a planar straight line drawing such that the vertices of one partite set of G lie on λe and the vertices of the other partite set lie on λi. We study radial planarity testing for bipartite graphs with the additional constraint that the edges are straight-line segments (two concentric circles are a special case of two parallel convex curves). The family of bipartite graphs which admit a planar straight-line drawing with the vertices constrained to be on two parallel convex curves and with no two vertices of the same partite set on different curves is characterized. The proof of sufficiency uses a linear time (real RAM) drawing algorithm in the case of two concentric circles
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