Coloring the complements of intersection graphs of geometric figures

Seog-Jin Kim, Kittikorn Nakprasit
2008 Discrete Mathematics  
Let G be the complement of the intersection graph G of a family of translations of a compact convex figure in R n . When n = 2, we show that (G) min{3 (G) − 2, 6 (G)}, where (G) is the size of the minimum dominating set of G. The bound on (G) 6 (G) is sharp. For higher dimension we show that (G) 2(n 2 − n + 1) 1/2 n−1 (n 2 − n + 1) 1/2 ( (G) − 1) + 1, for n 3. We also study the chromatic number of the complement of the intersection graph of homothetic copies of a fixed convex body in R n .
doi:10.1016/j.disc.2007.08.072 fatcat:ru7osgm3a5frzayje5mb7d6tly