Note on coloring of double disk graphs

The coloring of disk graphs is motivated by the frequency assignment problem. In 1998, Malesińska et al. introduced double disk graphs as their generalization. They showed that the chromatic number of a double disk graph G is at most 33 ω ( G ) - 35 , where ω ( G ) denotes the size of a maximum clique in G . Du et al. improved the upper bound to 31 ω ( G ) - 1 . In this paper we decrease the bound substantially; namely we show that the chromatic number of G is at most 15 ω ( G ) - 14 .