Dominator Chromatic Numbers of Orientations of Trees

Michael Cary

Published 2019-04-12Version 1

In this paper we prove that the dominator chromatic number of every oriented tree is invariant under reversal of orientation. In addition to this marquee result, we also prove the exact dominator chromatic number for arborescences and anti-arborescences as well as bounds on other orientations of oft studied tree topologies including generalized stars and caterpillars.