For given graphs and , the Turán number is defined to be the maximum number of edges in an -free subgraph of . Briggs and Cox introduced a dual version of this problem wherein for a given number , one maximizes the number of edges in a host graph for which . We resolve a problem of Briggs and Cox in the negative by showing that the inverse Turán number of is . More generally, we determine the order of magnitude of the inverse Turán number of for all and . Addressing another problem of Briggs and Cox, we determine the asymptotic value of the inverse Turán number of the paths of length and and provide an improved lower bound for all paths of even length. We also obtain improved bounds on the inverse Turán number of even cycles
Joint work with Ervin Győri, Nika Salia and Oscar Zamora.