Obstructions to some injective oriented colourings
Abstract
Each of several possible definitions of local injectivity for a homomorphism of an oriented graph G to an oriented graph H leads to an injective oriented colouring problem. For each case in which such a problem is solvable in polynomial time, we identify a set F of oriented graphs such that an oriented graph G has an injective oriented colouring with the given number of colours if and only if there is no F ∈ F for which there is a locally-injective homomorphism of F to G.
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