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How do you call a graph that the bipartite property is satisfied for the one set of nodes and not the other?

Say you have two set of nodes $A$ and $B$ where there can be edges between nodes of set $A$ but there can be no edges between nodes of set $B$.Of course there can be edges between nodes of different sets.Is there a name for this type of graph?

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  • $\begingroup$ No, there is no special name, and indeed you can do this for any graph (just take any independent set of vertices to form $B$ and the rest of the vertices form $A$). $\endgroup$ Dec 7 '20 at 11:28
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    $\begingroup$ That could be any graph, right? Let $G$ be any graph, let $B$ be any independent set of nodes (no edges between them) in $G$, and let $A$ be the rest of the nodes in $G$. $\endgroup$
    – bof
    Dec 7 '20 at 11:29
  • $\begingroup$ You could say that this holds iff $A$ is a vertex cover of the entire graph if that helps. $\endgroup$ Dec 7 '20 at 19:20
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This is more a characteristic of $B$. A subset $B$ of the nodes of a graph that have no edges between each other is called an independent set.

To further elaborate:

Every independent subset fulfills the criterion of the question, and every $B$ that fulfills the criterion of the question is inversely an independent subset.

Note that there are actually no criteria on $A$ other that it's the remaining graph, after removing $B$.

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