The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.

hinerD ¤ yF nd ulusm D hF nd i oule uD gF nd iesD fF @PHISA 9gontr tion lo kers for gr phs with for idden indu ed p thsF9D in elgorithms nd omplexity X Wth sntern tion l gonferen eD gseg PHISD risD pr n eD w y PHEPPD PHIS Y pro eedingsF D ppF IWREPHUF ve ture notes in omputer s ien eF @WHUWAF Further information on publisher's website:Publisher's copyright statement:The nal publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-18173-814.Additional information: Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Abstract. We consider the following problem: can a certain graph parameter of some given graph be reduced by at least d for some integer d via at most k edge contractions for some given integer k? We examine three graph parameters: the chromatic number, clique number and independence number. For each of these graph parameters we show that, when d is part of the input, this problem is polynomial-time solvable on P4-free graphs and NP-complete as well as W[1]-hard, with parameter d, for split graphs. As split graphs form a subclass of P5-free graphs, both results together give a complete complexity classification for Pfree graphs. The W[1]-hardness result implies that it is unlikely that the problem is fixed-parameter tractable for split graphs with parameter d. But we do show, on the positive side, that the problem is polynomialtime solvable, for each parameter, on split graphs if d is fixed, i.e., not part of the input. We also initiate a study into other subclasses of perfect graphs, namely cobipartite graphs and interval graphs.

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