Chromatic Numbers of Suborbital Graphs for Some Hecke Groups

Woratham Khangtragool, Khuanchanok Chaichana

Abstract

In this paper, we study the chromatic numbers of suborbital graphs for Hecke groups $H(\sqrt 2)$ and $H(\sqrt 3)$. We decompose each suborbital graph into disjoint isomorphic subgraphs and show that each subgraph is homomorphic to the Farey graph. Finally, we show that each suborbital graph has chromatic number 2 or 3.