On the two-dimensional orthogonal drawing of series-parallel graphs

Authors:
Satoshi Tayu;Kumiko Nomura;Shuichi Ueno
Affiliations:
Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, 152-8550-S3-57, Japan;Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, 152-8550-S3-57, Japan;Department of Communications and Integrated Systems, Tokyo Institute of Technology, Tokyo, 152-8550-S3-57, Japan
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

It has been known that every planar 4-graph has a 2-bend 2-D orthogonal drawing, with the only exception being the octahedron, every planar 3-graph has a 1-bend 2-D orthogonal drawing with the only exception being K"4, and every outerplanar 3-graph with no triangles has a 0-bend 2-D orthogonal drawing. We show in this paper that every series-parallel 4-graph has a 1-bend 2-D orthogonal drawing.