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Small grid drawings of planar graphs with balanced partition

Author

Listed:
  • Xiao Zhou

    (Tohoku University)

  • Takashi Hikino

    (Tohoku University)

  • Takao Nishizeki

    (Kwansei Gakuin University)

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 (

Suggested Citation

  • Xiao Zhou & Takashi Hikino & Takao Nishizeki, 2012. "Small grid drawings of planar graphs with balanced partition," Journal of Combinatorial Optimization, Springer, vol. 24(2), pages 99-115, August.
    • Handle: RePEc:spr:jcomop:v:24:y:2012:i:2:d:10.1007_s10878-011-9381-7
    DOI: 10.1007/s10878-011-9381-7
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