We address the parameterized complexity of Max Colorable Induced Subgraph on perfect graphs. The problem asks for a maximum sized q-colorable induced subgraph of an input graph G. Yannakakis and Gavril [ IPL 1987 ] showed that this problem is NP-complete even on split graphs if q is part of input, but gave a n O(q) algorithm on chordal graphs. We first observe that the problem is W[2]-hard parameterized by q, even on split graphs. However, when parameterized by , the number of vertices in the

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... lution, we give two fixed-parameter tractable algorithms. -The first algorithm runs in time 5.44 (n + #α(G)) O(1) where #α(G) is the number of maximal independent sets of the input graph. -The second algorithm runs in time q +o( ) n O(1) Tα where Tα is the time required to find a maximum independent set in any induced subgraph of G. The first algorithm is efficient when the input graph contains only polynomially many maximal independent sets; for example split graphs and co-chordal graphs. The second algorithm is FPT in alone, since q ≤ for all non-trivial situations. Finally, we show that (under standard complexity-theoretic assumptions) the problem does not admit a polynomial kernel on split and perfect graphs in the following sense: (a) On split graphs, we do not expect a polynomial kernel if q is a part of the input. (b) On perfect graphs, we do not expect a polynomial kernel even for fixed values of q ≥ 2.