A Construction of Uniquely Colourable Graphs with Equal Colour Class Sizes

Samuel Mohr

doi:10.1016/j.dam.2020.11.015

paper

A Construction of Uniquely Colourable Graphs with Equal Colour Class Sizes

arXiv:2001.08801 · doi:10.1016/j.dam.2020.11.015

Abstract

A uniquely $k$ -colourable graph is a graph with exactly one partition of the vertex set into at most $k$ colour classes. Here, we investigate some constructions of uniquely $k$ -colourable graphs and give a construction of $K_{k}$ -free uniquely $k$ -colourable graphs with equal colour class sizes.