Given graphs $G$, $H$ and $K$ and a homomorphism $$ G+K\to H+K $$ where $+$ denotes the join, does it follow that there also exists a graph homomorphism $G\to H$?
If this is known, I'd also appreciate a reference.
Given graphs $G$, $H$ and $K$ and a homomorphism $$ G+K\to H+K $$ where $+$ denotes the join, does it follow that there also exists a graph homomorphism $G\to H$?
If this is known, I'd also appreciate a reference.