Integer representations of convex polygon intersection graphs

Abstract. We study the grid size that is needed to represent intersection graphs of convex polygons. Here the polygons are similar to a base polygon P whose corners have rational coordinates and each corner of each polygon in the representation must lie on a point of the integer grid. We provide constructions to show that for intersection graphs of - translated copies of any fixed parallelogram a Ω(n2 ) × Ω(n2 ) grid is needed for some graphs; - translated copies of any other fixed convex polygon a 2Ω(n) × 2Ω(n) grid is needed for some graphs; - homothetic copies of any fixed convex polygon a 2Ω(n) × 2Ω(n) grid is needed for some graphs. We complement these results by giving a matching upper bound in each case.

• Type: Journal
• Year: 2011
• Where: COMPGEOM
• Authors: Tobias Müller, Erik Jan van Leeuwen, Jan van Leeuwen
• Keywords: COMPGEOM 2011, Convex Polygons, Discrete Geometry, Integer Grid, Intersection Graphs