A note on semi-transitivity of Mycielski graphs
Abstract
An orientation of a graph is semi-transitive if it contains no directed cycles and has no shortcuts. An undirected graph is semi-transitive if it can be oriented in a semi-transitive manner. The class of semi-transitive graphs includes several important graph classes. The Mycielski graph of an undirected graph is a larger graph constructed in a specific manner, which maintains the property of being triangle-free but increases the chromatic number. In this note, we prove Hameed's conjecture, which states that the Mycielski graph of a graph is semi-transitive if and only if is a bipartite graph. Notably, our solution to the conjecture provides an alternative and shorter proof of the Hameed's result on a complete characterization of semi-transitive extended Mycielski graphs.
Keywords
Cite
@article{arxiv.2408.05066,
title = {A note on semi-transitivity of Mycielski graphs},
author = {Sergey Kitaev and Artem Pyatkin},
journal= {arXiv preprint arXiv:2408.05066},
year = {2024}
}