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Communication Dans Un Congrès Année : 2015

Contraction Blockers for Graphs with Forbidden Induced Paths

Résumé

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 Pℓ-free 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 polynomial-time 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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Dates et versions

hal-01338229 , version 1 (01-02-2022)

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Öznur Diner, Daniel Paulusma, Christophe Picouleau, Bernard Ries. Contraction Blockers for Graphs with Forbidden Induced Paths. 9th International Conference on Algorithms and Complexity (CIAC 2015), May 2015, Paris, France. pp.194-207, ⟨10.1007/978-3-319-18173-8_14⟩. ⟨hal-01338229⟩
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