A Construction of Uniquely Colourable Graphs with Equal Colour Class Sizes

Samuel Mohr

doi:10.1016/j.dam.2020.11.015

A Construction of Uniquely Colourable Graphs with Equal Colour Class Sizes

Combinatorics 2020-11-23 v2

Authors: Samuel Mohr

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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.

Keywords

graph coloring rainbow coloring graph theory

Cite

@article{arxiv.2001.08801,
  title  = {A Construction of Uniquely Colourable Graphs with Equal Colour Class Sizes},
  author = {Samuel Mohr},
  journal= {arXiv preprint arXiv:2001.08801},
  year   = {2020}
}

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