Proximity Drawings of Outerplanar Graphs
GD '96 Proceedings of the Symposium on Graph Drawing
Proximity Constraints and Representable Trees
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
Handbook of Graph Drawing and Visualization (Discrete Mathematics and Its Applications)
Handbook of Graph Drawing and Visualization (Discrete Mathematics and Its Applications)
Polynomial area bounds for MST embeddings of trees
Computational Geometry: Theory and Applications
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A straight-line drawing of a plane graph G is a drawing of G where each vertex is drawn as a point and each edge is drawn as a straight-line segment without edge crossings. A proximity drawing Γ of a plane graph G is a straight-line drawing of G with the additional geometric constraint that two vertices of G are adjacent if and only if no other vertex of G is drawn in Γ within a "proximity region" of these two vertices in Γ. Depending upon how the proximity region is defined, a given plane graph G may or may not admit a proximity drawing. In one class of proximity drawings, known as β-drawings, the proximity region is defined in terms of a parameter β, where β Ɛ [0, ∞). A plane graph G is β-drawable if G admits a β-drawing. A sufficient condition for a biconnected 2-outerplane graph G to have a β-drawing is known. However, the known algorithm for testing the sufficient condition takes time O(n2). In this paper, we give a linear-time algorithm to test whether a biconnected 2-outerplane graph G satisfies the known sufficient condition or not. This consequently leads to a linear algorithm for β-drawing of a wide subclass of biconnected 2-outerplane graphs.