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Discrete Mathematics
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Discrete Mathematics
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Oriented graph coloring

Authors: Eric Sopena;

Oriented graph coloring

Abstract

An orientation of a graph \(H\) is a digraph obtained from \(H\) by giving to each edge one of its two possible orientations. A digraph \(G\) is an oriented graph if it is an orientation of some graph \(H\). An oriented \(k\)-coloring of an oriented graph \(G\) is a partition of the vertex set of \(G\) into \(k\) color classes such that no two adjacent vertices belong to the same color class and all the arcs linking two color classes have the same direction. The oriented chromatic number of an oriented graph \(G\) is the smallest \(k\) such that \(G\) has an oriented \(k\)-coloring. The oriented chromatic number of a graph \(H\) is the maximum of the oriented chromatic numbers of its orientations. This paper surveys the main results on oriented chromatic numbers.

Keywords

oriented graph, oriented graph coloring, Directed graphs (digraphs), tournaments, directed graph, acyclic chromatic number, planar graphs, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science, Coloring of graphs and hypergraphs, graph homomorphism, Discrete Mathematics and Combinatorics

  • BIP!
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    citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    52
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 10%
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
52
Top 10%
Top 10%
Top 10%
hybrid