The K4,6K_{4,6} extremal-number conjecture

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Let ex⁡(n,K4,6)\operatorname{ex}(n,K_{4,6}) be the maximum number of edges in an nn-vertex graph containing no copy of K4,6K_{4,6}. K4,6K_{4,6} extremal-number conjecture.

ex⁡(n,K4,6)=o(n7/4).\operatorname{ex}(n,K_{4,6})=o(n^{7/4}).

The conjecture reflects the authors' belief that the geometric restrictions in the projective norm graph represent the limit of what algebraic constructions can offer, despite the occurrence of K4,6K_{4,6} in NG⁡(q,4)\operatorname{NG}(q,4); proving the asserted little-oh improvement remains open.

References

Primary source

Tamás Mészáros, Lajos Rónyai and Tibor Szabó, “Singer difference sets and the projective norm graph”, arXiv:1908.05591 (2019).

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