TY - GEN

T1 - Grid drawings and the chromatic number

AU - Balko, Martin

PY - 2013/2/26

Y1 - 2013/2/26

N2 - 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.

AB - 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.

KW - chromatic number

KW - graph coloring

KW - graph drawings

KW - grid

UR - http://www.scopus.com/inward/record.url?scp=84874134498&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-36763-2_28

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

M3 - Conference contribution

AN - SCOPUS:84874134498

SN - 9783642367625

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 315

EP - 326

BT - Graph Drawing - 20th International Symposium, GD 2012, Revised Selected Papers

T2 - 20th International Symposium on Graph Drawing, GD 2012

Y2 - 19 September 2012 through 21 September 2012

ER -