Retracts of hypercubes

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Abstract
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.

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