Small grid drawings of planar graphs with balanced partition

Xiao Zhou, Takashi Hikino, Takao Nishizeki

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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 G1 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 (< (2/3) 2n 2).

Original languageEnglish
Pages (from-to)99-115
Number of pages17
JournalJournal of Combinatorial Optimization
Volume24
Issue number2
DOIs
Publication statusPublished - 2012 Aug

Keywords

  • Grid drawing
  • Partition
  • Planar graph
  • Series-parallel graph

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics

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