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 10p c + 34 corners, where p c is the number of vertices of degree 4 in the cycle c.
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References
d’Amore, F., Franciosa, P.G.: On the optimal binary plane partition for sets of isothetic rectangles. Information Proc. Letters 44, 255–259 (1992)
de Berg, M., Speckmann, B., Mumford, E.: On Rectilinear Duals for Vertex-Weighted Plane Graphs. In: Healy, P., Nikolov, N.S. (eds.) GD 2005. LNCS, vol. 3843, pp. 61–72. Springer, Heidelberg (2006)
Di Battista, G., et al.: Graph drawing: Algorithms for the visualization of graphs. Prentice-Hall, Englewood Cliffs (1999)
Yen, H.-C., Lu, H.-I., Liao, C.-C.: Floor-Planning via Orderly Spanning Trees. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, Springer, Heidelberg (2002)
Nishizeki, T., Miura, K., Rahman, M.S.: Algorithms for drawing plane graphs. IEICE Trans. Electron. E87-D(2), 281–289 (2004)
Rahman, M.S., Miura, K., Nishizeki, T.: Octagonal drawings of plane graphs with prescribed face areas. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds.) WG 2004. LNCS, vol. 3353, pp. 320–331. Springer, Heidelberg (2004)
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Kawaguchi, A., Nagamochi, H. (2007). Orthogonal Drawings for Plane Graphs with Specified Face Areas. In: Cai, JY., Cooper, S.B., Zhu, H. (eds) Theory and Applications of Models of Computation. TAMC 2007. Lecture Notes in Computer Science, vol 4484. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72504-6_53
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DOI: https://doi.org/10.1007/978-3-540-72504-6_53
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72503-9
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