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A tropical graph ( H , c ) consists of a graph H and a (not necessarily proper) vertex-colouring c of H . Given two tropical graphs ( G , c 1 ) and ( H , c ) , a homomorphism of ( G , c 1 ) to ( H , c ) is a standard graph homomorphism of G to H that also preserves the vertex-colours. We initiate the study of the computational complexity of tropical graph homomorphism...
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