Abstract
For a graph G, OAL G asks whether or not an input graph H together with a partial map g :S→G , S⊆ V( H), admits a homomorphism f :H→G such that f| S = g. We show that for connected graphs G 1, G 2, OAL G 1× G 2 is in P if G 1 and G 2 are trees and NP-complete otherwise.
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