Grid drawings and the chromatic number

Martin Balko

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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 Pen{combining double acute accent}aloza 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 Pen{combining double acute accent}aloza and F. J. Zaragoza Martinez.

Original languageEnglish
Title of host publicationGraph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers
Pages315-326
Number of pages12
DOIs
StatePublished - 26 Feb 2013
Externally publishedYes
Event20th International Symposium on Graph Drawing, GD 2012 - Redmond, WA, United States
Duration: 19 Sep 201221 Sep 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7704 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference20th International Symposium on Graph Drawing, GD 2012
Country/TerritoryUnited States
CityRedmond, WA
Period19/09/1221/09/12

Keywords

  • chromatic number
  • graph coloring
  • graph drawings
  • grid

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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