Grid representations and the chromatic number

Martin Balko

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A grid drawing of a graph maps vertices to the grid Zd and edges to line segments that avoid grid points representing other vertices. We show that a graph G is qd-colorable, d, q≥2, if and only if there is a grid drawing of G in Zd in which no line segment intersects more than q grid points. This strengthens the result of D. Flores Penaloza and F.J. Zaragoza Martinez. Second, we study grid drawings with a bounded number of columns, introducing some new NP-complete problems. Finally, we show that any planar graph has a planar grid drawing where every line segment contains exactly two grid points. This result proves conjectures asked by D. Flores Penaloza and F.J. Zaragoza Martinez.

Original languageEnglish
Pages (from-to)990-1002
Number of pages13
JournalComputational Geometry: Theory and Applications
Volume46
Issue number8
DOIs
StatePublished - 22 May 2013
Externally publishedYes

Keywords

  • Chromatic number
  • Graph coloring
  • Graph drawings
  • Grid

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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