An Experimental Evaluation of a Function in Extremal Combinatorics

We investigate the validity of a candidate formula for an extremal function introduced by Ferrara et al. The function is defined to be the minimum degree sum such that every bigraphic pair with a given number of terms in each part and at least this degree sum is guaranteed to have a realization that contains a complete bipartite subgraph of a given size. We show that the formula is valid for some input ranges and invalid for other input ranges. We also show that the difference between the true function value and that given by the formula can be arbitrarily large and conjecture that it may be NP-hard to compute the function value.