A coloring of the points of a poset P is proper if each color class induces an antichain, and distinguishing if the only automorphism of P that preserves colors is the identity. The distinguishing chromatic number of a poset, is the least integer for which there is a coloring of P that is both proper and distinguishing. In this talk we determine the distinguishing chromatic number when P is the sum of chains and discuss upper bounds in more general settings. We also make a connection to a scheduling application.
The Distinguishing Chromatic Number of a Poset
Ann Trenk, Wellesley CollegeAuthors: Karen Collins and Ann Trenk
2022 AWM Research Symposium
Advances in Combinatorics