TY - JOUR

T1 - A FIXED-PARAMETER TRACTABLE ALGORITHM for ELIMINATION DISTANCE to BOUNDED DEGREE GRAPHS

AU - Agrawal, Akanksha

AU - Kanesh, Lawqueen

AU - Panolan, Fahad

AU - Ramanujan, M. S.

AU - Saurabh, Saket

N1 - Publisher Copyright:
© 2022 Society for Industrial and Applied Mathematics

PY - 2022/1/1

Y1 - 2022/1/1

N2 - 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.

AB - 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.

KW - elimination distance

KW - fixed-parameter tractability

KW - graph modification

UR - http://www.scopus.com/inward/record.url?scp=85130591302&partnerID=8YFLogxK

U2 - 10.1137/21M1396824

DO - 10.1137/21M1396824

M3 - Article

AN - SCOPUS:85130591302

SN - 0895-4801

VL - 36

SP - 911

EP - 921

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 2

ER -