Grid drawings and the chromatic number

Martin Balko

doi:10.1007/978-3-642-36763-2_28

Grid drawings and the chromatic number

Martin Balko

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A grid drawing of a graph maps vertices to the grid ℤ^d and edges to line segments that avoid grid points representing other vertices. We show that a graph G is q^d-colorable, d, q ≥ 2, if and only if there is a grid drawing of G in ℤ^d 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 language	English
Title of host publication	Graph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers
Pages	315-326
Number of pages	12
DOIs	https://doi.org/10.1007/978-3-642-36763-2_28
State	Published - 26 Feb 2013
Externally published	Yes
Event	20th International Symposium on Graph Drawing, GD 2012 - Redmond, WA, United States Duration: 19 Sep 2012 → 21 Sep 2012

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	7704 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	20th International Symposium on Graph Drawing, GD 2012
Country/Territory	United States
City	Redmond, WA
Period	19/09/12 → 21/09/12

Keywords

chromatic number
graph coloring
graph drawings
grid

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science (all)

Access to Document

10.1007/978-3-642-36763-2_28

Cite this

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title = "Grid drawings and the chromatic number",

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.",

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Balko, M 2013, Grid drawings and the chromatic number. in Graph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7704 LNCS, pp. 315-326, 20th International Symposium on Graph Drawing, GD 2012, Redmond, WA, United States, 19/09/12. https://doi.org/10.1007/978-3-642-36763-2_28

Grid drawings and the chromatic number. / Balko, Martin.

Graph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers. 2013. p. 315-326 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7704 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Grid drawings and the chromatic number

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

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