A FIXED-PARAMETER TRACTABLE ALGORITHM for ELIMINATION DISTANCE to BOUNDED DEGREE GRAPHS

Akanksha Agrawal, Lawqueen Kanesh, Fahad Panolan, M. S. Ramanujan, Saket Saurabh

Research output: Contribution to journalArticlepeer-review

Abstract

In the literature on parameterized graph problems, there has been an increased effort in recent years aimed at exploring novel notions of graph edit-distance that are more powerful than the size of a modulator to a specific graph class. In this line of research, Bulian and Dawar [Algorithmica, 75 (2016), pp. 363-382] introduced the notion of elimination distance and showed that deciding whether a given graph has elimination distance at most k to any minor-closed class of graphs is fixed-parameter tractable parameterized by k [Algorithmica, 79 (2017), pp. 139-158]. They showed that graph isomorphism parameterized by the elimination distance to bounded degree graphs is fixed-parameter tractable and asked whether determining the elimination distance to the class of bounded degree graphs is fixed-parameter tractable. Recently, Lindermayr, Siebertz, and Vigny [MFCS 2020, LIPIcs Leibniz Int. Proc. Inform. 170, Wadern Germany, 2020, 65] obtained a fixed-parameter algorithm for this problem in the special case where the input is restricted to K5-minor free graphs. In this paper, we answer the question of Bulian and Dawar in the affirmative for general graphs. In fact, we give a more general result capturing elimination distance to any graph class characterized by a finite set of graphs as forbidden induced subgraphs.

Original languageEnglish
Pages (from-to)911-921
Number of pages11
JournalSIAM Journal on Discrete Mathematics
Volume36
Issue number2
DOIs
StatePublished - 1 Jan 2022
Externally publishedYes

Keywords

  • elimination distance
  • fixed-parameter tractability
  • graph modification

ASJC Scopus subject areas

  • Mathematics (all)

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