We study the computational complexity of $c$-Colored $P_\ell$ Deletion and $c$. Deletions . We show that both problems are fixed-parameter tractable with respect to the colored neighborhood diversity of the input graph . We also provide hardness results to outline the limits ofparameterization by the standard parameter solution size $k$. Finally, weconsider bicolored input graphs and show a special case of $2$-colored $4$Deletion that can be solved in polynomial time . We then analyze theparameterized complexity of these problems. We also show that $2”-coloured$P _4\$

Author(s) : Nils Jakob Eckstein, Niels Grüttemeier, Christian Komusiewicz, Frank Sommer