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{
    "pk": 64857,
    "title": "Inducibility and universality for trees",
    "subtitle": null,
    "abstract": "We answer three questions posed by Bubeck and Linial on the limit densities of subtrees in trees. We prove there exist positive \\(\\varepsilon_1\\) and \\(\\varepsilon_2\\) such that every tree that is neither a path nor a star has inducibility at most \\(1-\\varepsilon_1\\), where the inducibility of a tree \\(T\\) is defined as the maximum limit density of \\(T\\), and that there are infinitely many trees with inducibility at least \\(\\varepsilon_2\\). Finally, we construct a universal sequence of trees; that is, a sequence in which the limit density of any tree is positive.\n \nMathematics Subject Classifications: 05C05, 05C35\n \nKeywords: Trees, inducibility, graph density",
    "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": "Trees"
        },
        {
            "word": "inducibility"
        },
        {
            "word": "graph density"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/9gd4317z",
    "frozenauthors": [
        {
            "first_name": "Timothy",
            "middle_name": "F. N.",
            "last_name": "Chan",
            "name_suffix": "",
            "institution": "School of Mathematics, Monash University, Melbourne, Australia, and Mathematics Institute, University of Warwick, Coventry, U.K.",
            "department": ""
        },
        {
            "first_name": "Daniel",
            "middle_name": "",
            "last_name": "Král'",
            "name_suffix": "",
            "institution": "Faculty of Informatics, Masaryk University, Botanická 68A, 602 00 Brno, Czech Republic",
            "department": ""
        },
        {
            "first_name": "Bojan",
            "middle_name": "",
            "last_name": "Mohar",
            "name_suffix": "",
            "institution": "Department of Mathematics, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada",
            "department": ""
        },
        {
            "first_name": "David",
            "middle_name": "R.",
            "last_name": "Wood",
            "name_suffix": "",
            "institution": "School of Mathematics, Monash University, Melbourne, Australia",
            "department": ""
        }
    ],
    "date_submitted": "2022-10-11T15:07:35Z",
    "date_accepted": "2022-10-11T15:07:35Z",
    "date_published": "2022-10-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64857/galley/49667/download/"
        }
    ]
}