  The Maximum Weight Independent Set (MWIS) problem on finite undirected graphs
with vertex weights asks for a set of pairwise nonadjacent vertices of maximum
weight sum. MWIS is one of the most investigated and most important algorithmic
graph problems; it is well known to be NP-complete, and it remains NP-complete
even under various strong restrictions such as for triangle-free graphs. Its
complexity for $P_k$-free graphs, $k \ge 7$, is an open problem. In
\cite{BraMos2018}, it is shown that MWIS can be solved in polynomial time for
($P_7$,triangle)-free graphs. This result is extended by Maffray and Pastor
\cite{MafPas2016} showing that MWIS can be solved in polynomial time for
($P_7$,bull)-free graphs. In the same paper, they also showed that MWIS can be
solved in polynomial time for ($S_{1,2,3}$,bull)-free graphs.
  In this paper, using a similar approach as in \cite{BraMos2018}, we show that
MWIS can be solved in polynomial time for ($S_{1,2,4}$,triangle)-free graphs
which generalizes the result for ($P_7$,triangle)-free graphs.
