We say that a property $\Pi$ is hereditary if whenever $G=(V,E)$ satisfies $\Pi$ then any induced subgraph $G[V']$ (with $V' \subseteq V $) satisfies $\Pi$.
I was wondering whether there is a proper name for the same concept when restricted to bipartite graphs. For example:
Given a bipartite graph G=(V,W,E), where V and W are the two independent sets of vertices, we call a property $\Pi$ "V-hereditary" (resp. "W-hereditary") if whenever $G$ satisfies $\Pi$ then any induced subgraph $G[V' \cup W]$ (resp. $G[V \cup W']$) satisfies $\Pi$ (with $V' \subseteq V$ and $W' \subseteq W'$).
Thank you very much!
EDIT I corrected the question after Oliver observation. The idea is that I allow removal only from one of the two sets.