We consider in this talk the scheduling problem $P\vert prec, p_j = 1 \vert C_{\max}$.
Let $k$ denote the degeneracy of the co-comparability graph $H_G$ associated with the precedence constraint graph $G$.
We show that this scheduling problem is Fixed-Parameter Tractable (FPT) when parameterized by $k$.
First, we show that partial schedules correspond to cliques of $H_G$, and that the number of such cliques is in ${\cal O}(n \cdot 3^k)$.
Then, we derive a dynamic programming algorithm with a time complexity of ${\cal O}(n^3 + k^2 n^2 3^{2k})$ for $P\vert prec, p_j = 1 \vert C_{\max}$.