On the CNF-complexity of bipartite graphs containing no $K_{2,2}$ 's

preprint2012arXivOpen access

By a probabilistic construction, we find a bipartite graph having average degree $d$ which can be expressed as a conjunctive normal form using $C \log d$ clauses. This contradicts research problem 1.33 of Jukna.

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On the CNF-complexity of bipartite graphs containing no $K_{2,2}$ 's

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On the CNF-complexity of bipartite graphs containing no K2,2K_{2,2}K2,2​'s

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On the CNF-complexity of bipartite graphs containing no $K_{2,2}$ 's