Additive Approximation of Generalized Turán Questions

Noga Alon, Clara Shikhelman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)464-481
Number of pages18
JournalAlgorithmica
Volume84
Issue number2
DOIs
StatePublished - Feb 2022

Funding

FundersFunder number
National Science FoundationDMS-1855464
German-Israeli Foundation for Scientific Research and DevelopmentG-1347-304.6/2016
United States-Israel Binational Science Foundation2018267
Israel Science Foundation281/17

    Keywords

    • Generalized Turan problems
    • Graph approximation algorithms
    • Graph modifications
    • Regularity lemma

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