{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article10441","name":"Independent Feedback Vertex Set for P_5-free Graphs","abstract":"The NP-complete problem Feedback Vertex Set is to decide if it is possible, for a given integer k>=0, to delete at most k vertices from a given graph so that what remains is a forest. The variant in which the deleted vertices must form an independent set is called Independent Feedback Vertex Set and is also NP-complete. In fact, even deciding if an independent feedback vertex set exists is NP-complete and this problem is closely related to the 3-Colouring problem, or equivalently, to the problem of deciding if a graph has an independent odd cycle transversal, that is, an independent set of vertices whose deletion makes the graph bipartite. We initiate a systematic study of the complexity of Independent Feedback Vertex Set for H-free graphs. We prove that it is NP-complete if H contains a claw or cycle. Tamura, Ito and Zhou proved that it is polynomial-time solvable for P_4-free graphs. We show that it remains in P for P_5-free graphs. We prove analogous results for the Independent Odd Cycle Transversal problem, which asks if a graph has an independent odd cycle transversal of size at most k for a given integer k>=0.","keywords":["feedback vertex set","odd cycle transversal","independent set","H-free graph"],"author":[{"@type":"Person","name":"Bonamy, Marthe","givenName":"Marthe","familyName":"Bonamy"},{"@type":"Person","name":"Dabrowski, Konrad K.","givenName":"Konrad K.","familyName":"Dabrowski"},{"@type":"Person","name":"Feghali, Carl","givenName":"Carl","familyName":"Feghali"},{"@type":"Person","name":"Johnson, Matthew","givenName":"Matthew","familyName":"Johnson"},{"@type":"Person","name":"Paulusma, Dani\u00ebl","givenName":"Dani\u00ebl","familyName":"Paulusma"}],"position":16,"pageStart":"16:1","pageEnd":"16:12","dateCreated":"2017-12-07","datePublished":"2017-12-07","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Bonamy, Marthe","givenName":"Marthe","familyName":"Bonamy"},{"@type":"Person","name":"Dabrowski, Konrad K.","givenName":"Konrad K.","familyName":"Dabrowski"},{"@type":"Person","name":"Feghali, Carl","givenName":"Carl","familyName":"Feghali"},{"@type":"Person","name":"Johnson, Matthew","givenName":"Matthew","familyName":"Johnson"},{"@type":"Person","name":"Paulusma, Dani\u00ebl","givenName":"Dani\u00ebl","familyName":"Paulusma"}],"copyrightYear":"2017","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.ISAAC.2017.16","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6295","volumeNumber":92,"name":"28th International Symposium on Algorithms and Computation (ISAAC 2017)","dateCreated":"2017-12-07","datePublished":"2017-12-07","editor":[{"@type":"Person","name":"Okamoto, Yoshio","givenName":"Yoshio","familyName":"Okamoto"},{"@type":"Person","name":"Tokuyama, Takeshi","givenName":"Takeshi","familyName":"Tokuyama"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article10441","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6295"}}}