Polynomial removal lemmas for ordered graphs

Lior Gishboliner, István Tomon

Research output: Contribution to journalArticlepeer-review


A recent result of Alon, Ben-Eliezer and Fischer establishes an induced removal lemma for ordered graphs. That is, if F is an ordered graph and ε > 0, then there exists δF (ε) > 0 such that every n-vertex ordered graph G containing at most δF (ε)nv(F) induced copies of F can be made induced F-free by adding/deleting at most εn2 edges. We prove that δF (ε) can be chosen to be a polynomial function of ε if and only if |V (F)| = 2, or F is the ordered graph with vertices x < y < z and edges {x, y}, {x, z} (up to complementation and reversing the vertex order). We also discuss similar problems in the noninduced case.

Original languageEnglish
Article number#3
JournalCombinatorial Theory
Issue number3
StatePublished - 2022
Externally publishedYes


  • Ordered graph
  • removal lemma


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