A Note on Plus-Contacts, Rectangular Duals, and Box-Orthogonal Drawings

08/31/2017

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by   Therese Biedl, et al.

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A plus-contact representation of a planar graph G is called c-balanced if for every plus shape +_v, the number of other plus shapes incident to each arm of +_v is at most c Δ +O(1), where Δ is the maximum degree of G. Although small values of c have been achieved for a few subclasses of planar graphs (e.g., 2- and 3-trees), it is unknown whether c-balanced representations with c<1 exist for arbitrary planar graphs. In this paper we compute (1/2)-balanced plus-contact representations for all planar graphs that admit a rectangular dual. Our result implies that any graph with a rectangular dual has a 1-bend box-orthogonal drawings such that for each vertex v, the box representing v is a square of side length deg(v)/2+ O(1).