Retracts of hypercubes

An induced subgraph G of a graph H is a retract of H if there is an edge‐preserving map f from H onto G such that f | G is the identity map on G . A median graph is a connected graph such that for any three vertices u,v and w , there exists a unique vertex x which lies simultaneously on some shortest ( u,v )‐, ( v,w )‐, and ( w,u )‐paths. It is shown that a graph G is a retract of some hypercube if and only if G is a median graph.