THE TURÁN NUMBER OF SPANNING STAR FORESTS

Let F be a family of graphs. The Turán number of F, denoted by ex(n, F), is the maximum number of edges in a graph with n vertices which does not contain any subgraph isomorphic to some graph in F. A star forest is a forest whose connected components are all stars and isolated vertices. Motivated by the results of Wang, Yang and Ning about the spanning Turán number of linear forests [J. Wang and W. Yang, The Turán number for spanning linear forests, Discrete Appl. Math. 254 (2019) 291–294; B. Ning and J. Wang, The formula for Turán number of spanning linear forests, Discrete Math. 343 (2020) #111924]. In this paper, let S_n,k be the set of all star forests with n vertices and k edges.