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Bipartite complete graph

Set

$V,E$ … set
$\langle V,E,\psi\rangle \in \mathrm{it}(E,V) $
$\langle V,E,\psi\rangle $ … undirected graph
$ X\cap Y=\emptyset $
$\exists X,Y.\ (\forall u,v.\ \{u,v\}\in\mathrm{im}(\psi)\implies (u\in X\land v\in Y)\lor (v\in X\land u\in Y)) \land (\forall(x\in X),(y\in Y).\ \{x,y\}\in\mathrm{im}\ \psi $

Discussion

Let $G$ be a bipartite complete graph with parts $X$ and $Y$. Then $G$ is bipartite complete if each $x\in X$ connects to each $y\in Y$.

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