Abstract: During the last decades, there has been a lot of research on the computational complexity of k-coloring in H- free graphs when H is a linear forest. It is known that k-coloring $K_1,3$ (claw) free graphs is NP-complete for $k\geq 3$.In this talk, we will study the techniques used by Barnaby Martin, Danil Paulusma and Siani Smith in 2021 to generalize this result for $K^r_1,3$ (subdivided claw) free graphs with bounded diameter.