Star-critical Ramsey number of Fn versus K4

For two graphs G and H, the Ramsey number r(G,H) is the smallest positive integer r, such that any red/blue coloring of the edges of graph Kr contains either a red subgraph that is isomorphic to G or a blue subgraph that is isomorphic to H. Let Sk=K1,k be a star of order k+1 and Kn⊔Sk be a graph obtained by adding a new vertex v and joining v to k vertices of Kn. The star-critical Ramsey number r∗(G,H) is the smallest positive integer k such that any red/blue coloring of the edges of graph Kr−1⊔Sk contains either a red subgraph that is isomorphic to G or a blue subgraph that is isomorphic to H where r=r(G,H). In this paper, it is shown that r∗(Fn,K4)=4n+2 where n≥4.