Description
For given graphs G and F, the Turán number ex(G,F) is defined to be the maximum number of edges in an F-free subgraph of G. Foucaud, Krivelevich and Perarnau and later independently Briggs and Cox introduced a dual version of this problem wherein for a given number k, one maximizes the number of edges in a host graph G for which ex(G,H)<k. Addressing a problem of Briggs and Cox, we determine the asymptotic value of the inverse Turán number of the paths of length 4 and 5 and provide an improved lower bound for all paths of even length. We also obtain bounds on the inverse Turán number of even cycles giving improved bounds on the leading coefficient in the case of C4.
Joint work with Ervin Győri, Casey Tompkins and Oscar Zamora.
https://zoom.us/j/91825186172?pwd=cllMY0pXMyt5emNqWWxtNVJrbjVodz09