Abstract
Oriented coloring of an oriented graph G is an arc-preserving homomorphism from G into a tournament H. We say that the graph H is universal for a family of oriented graphs mathcal {C} if for every Gin mathcal {C} there exists a homomorphism from G into H. We are interested in finding a universal graph for the family of orientations of cubic graphs. In this paper we present constructive proof that: if there exists a universal graph H on 7 vertices for every orientation of cubic graphs, then minimum out-degree and minimum in-degree of H are equal to 2. That gives a negative answer to the question presented in Pinlou’s PHD thesis.
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