On the Oriented Coloring of the Disjoint Union of Graphs

Coelho, Erika M. M.; Coelho, Hebert; Faria, Luérbio; Ferreira, Mateus de Paula; Gravier, Sylvain; Klein, Sulamita

doi:10.1007/978-3-030-79987-8_14

Lecture Notes in Computer Science

2021

DOI: 10.1007/978-3-030-79987-8_14

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On the Oriented Coloring of the Disjoint Union of Graphs

Erika M. M. Coelho

Hebert Coelho

Luérbio Faria

et al.

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2024

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On the oriented coloring of the disjoint union of graphs

Coelho,

Coelho da Silva,

Faria

et al. 2024

RAIRO-Oper. Res.

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Let [[EQUATION]] [[EQUATION]] be an oriented graph and [[EQUATION]] the underlying graph of [[EQUATION]]. An oriented k-coloring of [[EQUATION]] is a partition of [[EQUATION]] into k color classes, such that there is no pair of adjacent vertices belonging to the same class and all the arcs between a pair of color classes have the same orientation. The smallest k such that [[EQUATION]] admits an oriented k-coloring is the oriented chromatic number [[EQUATION]] = k of [[EQUATION]]. The oriented chromatic number [[EQUATION]] of the undirected graph [[EQUATION]] is the maximum of [[EQUATION]] for all orientations [[EQUATION]] of [[EQUATION]]. Oriented chromatic number of product of two graphs [[EQUATION]] were widely studied, but the disjoint union [[EQUATION]] has not still been considered. In this article we proved bounds for the oriented chromatic number of any two oriented graphs and we also proved that given two complete graphs [[EQUATION]] and [[EQUATION]] with [[EQUATION]], there is a real number [[EQUATION]] such that [[EQUATION]]. Additionally, we established exact values of the union of one complete graph with one cycle and of one complete graph with a forest.

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On the oriented coloring of the disjoint union of graphs

Coelho,

Coelho da Silva,

Faria

et al. 2024

RAIRO-Oper. Res.

View full text Add to dashboard Cite

show abstract

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On the Oriented Coloring of the Disjoint Union of Graphs

Cited by 1 publication

References 13 publications

On the oriented coloring of the disjoint union of graphs

On the oriented coloring of the disjoint union of graphs

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