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{
    "pk": 64858,
    "title": "Polynomial removal lemmas for ordered graphs",
    "subtitle": null,
    "abstract": "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 \\(\\varepsilon›0\\), then there exists  \\(\\delta_{F}(\\varepsilon)›0\\) such that every \\(n\\)-vertex ordered graph  \\(G\\) containing at most \\(\\delta_{F}(\\varepsilon) n^{v(F)}\\) induced  copies of \\(F\\) can be made induced \\(F\\)-free by adding/deleting at  most \\(\\varepsilon n^2\\) edges. We prove that  \\(\\delta_{F}(\\varepsilon)\\) can be chosen to be a polynomial function of  \\(\\varepsilon\\) 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 non-induced case.\n \nMathematics Subject Classifications: 05C35, 05C75\n \nKeywords: Ordered graph, removal lemma",
    "language": "en",
    "license": {
        "name": "Creative Commons Attribution 4.0",
        "short_name": "CC BY 4.0",
        "text": "Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.",
        "url": "https://creativecommons.org/licenses/by/4.0"
    },
    "keywords": [
        {
            "word": "Ordered graph"
        },
        {
            "word": "removal lemma"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/7xw1r1rw",
    "frozenauthors": [
        {
            "first_name": "Lior",
            "middle_name": "",
            "last_name": "Gishboliner",
            "name_suffix": "",
            "institution": "Department of Mathematics, ETH Zurich, Switzerland",
            "department": ""
        },
        {
            "first_name": "István",
            "middle_name": "",
            "last_name": "Tomon",
            "name_suffix": "",
            "institution": "Department of Mathematics, ETH Zurich, Switzerland",
            "department": ""
        }
    ],
    "date_submitted": "2022-10-11T15:46:27Z",
    "date_accepted": "2022-10-11T15:46:27Z",
    "date_published": "2022-10-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64858/galley/49668/download/"
        }
    ]
}