The Independent Set Problem Is FPT for Even-Hole-Free Graphs
The class of even-hole-free graphs is very similar to the class of perfect graphs, and was indeed a cornerstone in the tools leading to the proof of the Strong Perfect Graph Theorem. However, the complexity of computing a maximum independent set (MIS) is a long-standing open question in even-hole-free graphs. From the hardness point of view, MIS is W[1]-hard in the class of graphs without induced 4-cycle (when parameterized by the solution size). Halfway of these, we show in this paper that MIS is FPT when parameterized by the solution size in the class of even-hole-free graphs. The main idea is to apply twice the well-known technique of augmenting graphs to extend some initial independent set.
independent set
FPT algorithm
even-hole-free graph
augmenting graph
Theory of computation~Graph algorithms analysis
Theory of computation~Fixed parameter tractability
21:1-21:12
Regular Paper
The second and third named authors are partially supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).
The majority of paper was prepared while the first named author was a student at ENS de Lyon.
Edin
Husić
Edin Husić
Department of Mathematics, LSE, Houghton Street, London, WC2A 2AE, United Kingdom
Stéphan
Thomassé
Stéphan Thomassé
Univ Lyon, CNRS, ENS de Lyon, Université Claude Bernard Lyon 1, LIP UMR5668, France
Institut Universitaire de France, Paris, France
Nicolas
Trotignon
Nicolas Trotignon
Univ Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, CNRS, LIP, F-69342, Lyon Cedex 07, France
10.4230/LIPIcs.IPEC.2019.21
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Edin Husić, Stéphan Thomassé, and Nicolas Trotignon
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