Stability from graph symmetrisation arguments with applications to inducibility

Abstract

AbstractWe present a sufficient condition for the stability property of extremal graph problems that can be solved via Zykov's symmetrisation. Our criterion is stated in terms of an analytic limit version of the problem. We show that, for example, it applies to the inducibility problem for an arbitrary complete bipartite graph , which asks for the maximum number of induced copies of in an ‐vertex graph, and to the inducibility problem for and , the only complete partite graphs on at most five vertices for which the problem was previously open.