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DOI: 10.7155/jgaa.00316
1Bend Orthogonal Partial Edge Drawing
Vol. 18, no. 1, pp. 111131, 2014. Regular paper.
Abstract Recently, a new layout style to avoid edge crossings in straightline drawings of nonplanar graphs received attention. In a Partial Edge Drawing (PED), the middle part of each segment representing an edge is dropped and the two remaining parts, called stubs, are not crossed. To help the user inferring the position of the two endvertices of each edge, additional properties like symmetry and homogeneity are ensured in a PED. In this paper we explore this approach with respect to orthogonal drawings  a central concept in graph drawing. In particular, we focus on orthogonal drawings with one bend per edge, i.e., 1bend drawings, and we define a new model called 1bend Orthogonal Partial Edge Drawing, or simply 1bend OPED. Similarly to the straightline case, we study those graphs that admit 1bend OPEDs when homogeneity and symmetry are required, where these two properties are defined so to support readability and avoid ambiguities. According to this new model, we show that every graph that admits a 1bend drawing also admits a 1bend OPED as well as 1bend homogeneous orthogonal PED, i.e., a 1bend HOPED. Furthermore, we prove that all graphs with maximum degree 3 admit a 1bend symmetric and homogeneous orthogonal PED, i.e., a 1bend SHOPED. Concerning graphs with maximum degree 4, we prove that the 2circulant graphs that admit a 1bend drawing also admit a 1bend SHOPED, while there is a graph with maximum degree 4 that does not admit such a representation.

Submitted: August 2013.
Reviewed: November 2013.
Revised: November 2013.
Accepted: January 2014.
Final: January 2014.
Published: January 2014.
Communicated by
Csaba D. Tóth
