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May 4 at 14:35 comment added LSpice You changed notation from $(n, m)$ to $(p, q)$ for the cardinality of the ‘parts’, and I think in one place made an accidental inconsistency: $f(G)$ maximises $p q$, but you had $\lvert V'\rvert = m$. I edited to require $\lvert V'\rvert = q$, as the context suggested. I hope that this was all right. \\ When defining $f(n, m, k)$, you do not want to require that $p = n$ or $q = m$, or that each vertex of $U'$ have degree $k$?
May 4 at 14:33 history edited LSpice CC BY-SA 4.0
Typos
May 4 at 12:54 comment added Fedor Petrov We have $f(n, m, k)\geqslant \max(k,kn/m) $ that corresponds to $\min(p, q)=1$. I expect this to be tight for not too large $k$.
May 4 at 12:39 history asked user119197 CC BY-SA 4.0