DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

Journal Impact Factor (JIF 2022): 0.7

5-year Journal Impact Factor (2022): 0.7

CiteScore (2022): 1.9

SNIP (2022): 0.902

Discussiones Mathematicae Graph Theory

Article in volume

Authors:

A. Nenca

Anna Nenca

University of Gdańsk

email: anenca@inf.ug.edu.pl

Title:

Oriented chromatic number for Cartesian products $P_m\Box P_n$ and $C_m\Box P_n$

PDF

Source:

Discussiones Mathematicae Graph Theory 42(3) (2022) 799-810

Received: 2019-06-05 , Revised: 2020-01-31 , Accepted: 2020-02-03 , Available online: 2020-02-24 , https://doi.org/10.7151/dmgt.2307

Abstract:

\( \newcommand{\ora}{\overrightarrow} \)We consider oriented chromatic number of Cartesian products of two paths $P_m\Box P_n$ and of Cartesian products of paths and cycles, $C_m\Box P_n$. We say that the oriented graph $\overrightarrow G$ is colored by an oriented graph $\ora H$ if there is a homomorphism from $\ora G$ to $\overrightarrow H$. In this paper we show that there exists an oriented tournament $\overrightarrow H_{10}$ with ten vertices which colors every orientation of $P_8 \Box P_n$ and every orientation of $C_m \Box P_n$, for $m=3,4,5,6,7$ and $n\geq 1$. We also show that there exists an oriented graph $\overrightarrow T_{16}$ with sixteen vertices which colors every orientation of $C_m \Box P_n$.

Keywords:

graphs, oriented coloring, oriented chromatic number

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