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A homomorphism of an oriented graph to an oriented graph is a mapping from to such that is an arc in whenever is an arc in . A homomorphism of to is said to be -preserving for some oriented graph if for every connected subgraph of isomorphic to a subgraph of , is isomorphic to its homomorphic image in . The -preserving oriented chromatic number of an oriented graph is the minimum number of vertices in an oriented graph such that there exists a -preserving...
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