Small grid drawings of planar graphs with balanced partition

Xiao Zhou (), Takashi Hikino () and Takao Nishizeki ()
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Xiao Zhou: Tohoku University
Takashi Hikino: Tohoku University
Takao Nishizeki: Kwansei Gakuin University

Journal of Combinatorial Optimization, 2012, vol. 24, issue 2, No 3, 99-115

Abstract: Abstract In a grid drawing of a planar graph, every vertex is located at a grid point, and every edge is drawn as a straight-line segment without any edge-intersection. It is known that every planar graph G of n vertices has a grid drawing on an (n−2)×(n−2) or (4n/3)×(2n/3) integer grid. In this paper we show that if a planar graph G has a balanced partition then G has a grid drawing with small grid area. More precisely, if a separation pair bipartitions G into two edge-disjoint subgraphs G 1 and G 2, then G has a max {n 1,n 2}×max {n 1,n 2} grid drawing, where n 1 and n 2 are the numbers of vertices in G 1 and G 2, respectively. In particular, we show that every series-parallel graph G has a (2n/3)×(2n/3) grid drawing and a grid drawing with area smaller than 0.3941n 2 (

Keywords: Grid drawing; Planar graph; Series-parallel graph; Partition (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-011-9381-7

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