Misra, Neeldhara and Panolan, Fahad and Rai, Ashutosh and Raman, Venkatesh and Saurabh, Saket
(2013)
*Parameterized Algorithms for MAX COLORABLE INDUCED SUBGRAPH Problem on Perfect Graphs.*
In: 39th International Workshop on Graph-Theoretic Concepts in Computer Science (WG), JUN 19-21, 2013, Lubeck, GERMANY, pp. 370-381.

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## Abstract

We address the parameterized complexity ofMaxColorable 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 W2]-hard parameterized by q, even on split graphs. However, when parameterized by l, the number of vertices in the solution, we give two fixed-parameter tractable algorithms. The first algorithm runs in time 5.44(l) (n+#alpha(G))(O(1)) where #alpha(G) is the number of maximal independent sets of the input graph. The second algorithm runs in time q(l+o()l())n(O(1))T(alpha) where T-alpha 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 running time of the second algorithm is FPT in l alone (whenever T-alpha is a polynomial in n), since q <= l for all non-trivial situations. Finally, we show that (under standard complexitytheoretic 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.

Item Type: | Conference Proceedings |
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Series.: | Lecture Notes in Computer Science |

Publisher: | SPRINGER-VERLAG BERLIN |

Additional Information: | Copy right for this article belongs to the SPRINGER-VERLAG BERLIN, HEIDELBERGER PLATZ 3, D-14197 BERLIN, GERMANY |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Date Deposited: | 28 Nov 2014 05:47 |

Last Modified: | 28 Nov 2014 05:47 |

URI: | http://eprints.iisc.ac.in/id/eprint/50349 |

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