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Exact Values, Extremal Classifications, and Sum-of-Squares Reductions for Second-Order Zarankiewicz Numbers
There is a natural connection between the SOS rank problem for bi-quadratic forms and the Zarankiewicz extremal problem for C4-free bipartite graphs. The classical Zarankiewicz number z(m,n) controls the bipartite skeleton associated with monomial squares. Allowing two cells to form a single bilinea
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