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

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Keywords : colored - show - parameter - complexity - graphs -

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