Every orientation of a connected cubic graph has an oriented 8-coloring, and every orientation of a cubic graph has a 2-dipath 7-coloring.
A study on oriented relative clique number
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A Note on Colourings of Connected Oriented Cubic Graphs
Every orientation of a connected cubic graph has an oriented 8-coloring, and every orientation of a cubic graph has a 2-dipath 7-coloring.