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

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∆+O(1), where ∆ is the maximum degree of G. Although small values of c have been achieved for a few subclasses of planar graphs (e.g., 2and 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).