Maximum weight independent set for ℓclaw-free graphs in polynomial time

In this paper, using a dynamic programming approach (inspired by Farber's result about MWIS for 2K2-free graphs), we show that for any fixed ℓ, MWIS can be solved in polynomial time for ℓclaw-free graphs. This solves the open cases for MWIS on (P3+ claw)-free graphs and on (2K2+claw)-free graphs and extends known results for claw-free graphs, ℓK2-free graphs, (K2+claw)-free graphs, and ℓP3-free graphs.