  We revisit the recent polynomial-time algorithm for the MAX WEIGHT
INDEPENDENT SET (MWIS) problem in bounded-degree graphs that do not contain a
fixed graph whose every component is a subdivided claw as an induced subgraph
[Abrishami, Dibek, Chudnovsky, Rz\k{a}\.zewski, SODA 2022].
  First, we show that with an arguably simpler approach we can obtain a faster
algorithm with running time $n^{\mathcal{O}(\Delta^2)}$, where $n$ is the
number of vertices of the instance and $\Delta$ is the maximum degree. Then we
combine our technique with known results concerning tree decompositions and
provide a polynomial-time algorithm for MWIS in graphs excluding a fixed graph
whose every component is a subdivided claw as an induced subgraph, and a fixed
biclique as a subgraph.
