Orthogonal drawings for plane graphs with specified face areas

Authors:
Akifumi Kawaguchi;Hiroshi Nagamochi
Affiliations:
Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan
Venue:
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Year:
2007

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Abstract

We consider orthogonal drawings of a plane graph G with specified face areas. For a natural number k, a k-gonal drawing of G is an orthogonal drawing such that the outer cycle is drawn as a rectangle and each inner face is drawn as a polygon with at most k corners whose area is equal to the specified value. In this paper, we show that several classes of plane graphs have a k-gonal drawing with bounded k; A slicing graph has a 10-gonal drawing, a rectangular graph has an 18-gonal drawing and a 3-connected plane graph whose maximum degree is 3 has a 34- gonal drawing. Furthermore, we showed that a 3-connected plane graph G whose maximum degree is 4 has an orthogonal drawing such that each inner facial cycle c is drawn as a polygon with at most 10pc +34 corners, where pc is the number of vertices of degree 4 in the cycle c.