Tight concentration of star saturation number in random graphs

Abstract

For given graphs F and G, the minimum number of edges in an inclusion-maximal F-free subgraph of G is called the F-saturation number and denoted sat(G,F). For the star F=K1,r, the asymptotics of sat(G(n,p),F) is known. We prove a sharper result: whp sat(G(n,p),K1,r) is concentrated in a set of 2 consecutive points.