Tight concentration of star saturation number in random graphs

For given graphs F and G, the minimum number of edges in an inclusion-maximal Ffree 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.