Oriented chromatic number of Halin graphs

TL;DR

This paper proves that every Halin graph has an oriented chromatic number at most 8, improving previous bounds and confirming a conjecture, which advances understanding of graph colorings in oriented graphs.

Contribution

The paper establishes a new upper bound of 8 for the oriented chromatic number of Halin graphs, confirming a longstanding conjecture.

Findings

Oriented chromatic number of Halin graphs is at most 8

Improves previous upper bounds by Hosseini Dolama and Sopena

Confirms Vignal's conjecture

Abstract

Oriented chromatic number of an oriented graph $G$ is the minimum order of an oriented graph $H$ such that $G$ admits a homomorphism to $H$. The oriented chromatic number of an unoriented graph $G$ is the maximal chromatic number over all possible orientations of $G$. In this paper, we prove that every Halin graph has oriented chromatic number at most 8, improving a previous bound by Hosseini Dolama and Sopena, and confirming the conjecture given by Vignal.