TY - JOUR

T1 - Additive Approximation of Generalized Turán Questions

AU - Alon, Noga

AU - Shikhelman, Clara

N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022/2

Y1 - 2022/2

N2 - For graphs G and T, and a family of graphs F let ex (G, T, F) denote the maximum possible number of copies of T in an F-free subgraph of G. We investigate the algorithmic aspects of calculating and estimating this function. We show that for every graph T, finite family F and constant ϵ> 0 there is a polynomial time algorithm that approximates ex (G, T, F) for an input graph G on n vertices up to an additive error of ϵnv(T). We also consider the possibility of a better approximation, proving several positive and negative results, and suggesting a conjecture on the exact relation between T and F for which no significantly better approximation can be found in polynomial time unless P= NP.

AB - For graphs G and T, and a family of graphs F let ex (G, T, F) denote the maximum possible number of copies of T in an F-free subgraph of G. We investigate the algorithmic aspects of calculating and estimating this function. We show that for every graph T, finite family F and constant ϵ> 0 there is a polynomial time algorithm that approximates ex (G, T, F) for an input graph G on n vertices up to an additive error of ϵnv(T). We also consider the possibility of a better approximation, proving several positive and negative results, and suggesting a conjecture on the exact relation between T and F for which no significantly better approximation can be found in polynomial time unless P= NP.

KW - Generalized Turan problems

KW - Graph approximation algorithms

KW - Graph modifications

KW - Regularity lemma

UR - http://www.scopus.com/inward/record.url?scp=85122809467&partnerID=8YFLogxK

U2 - 10.1007/s00453-021-00899-4

DO - 10.1007/s00453-021-00899-4

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AN - SCOPUS:85122809467

SN - 0178-4617

VL - 84

SP - 464

EP - 481

JO - Algorithmica

JF - Algorithmica

IS - 2

ER -