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{
    "pk": 64933,
    "title": "Resilience for tight Hamiltonicity",
    "subtitle": null,
    "abstract": "We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. Specifically, for any \\(\\gamma›0\\) and \\(k\\ge3\\), we show that asymptotically almost surely, every subgraph of the binomial random \\(k\\)-uniform hypergraph \\(G^{(k)}\\big(n,n^{\\gamma-1}\\big)\\) in which all \\((k-1)\\)-sets are contained in at least \\(\\big(\\tfrac12+2\\gamma\\big)pn\\) edges has a tight Hamilton cycle. This is a cyclic ordering of the \\(n\\) vertices such that each consecutive \\(k\\) vertices forms an edge.\n \nMathematics Subject Classifications: 05C80, 05C35\n \nKeywords: Random graphs, hypergraphs, tight Hamilton cycles, resilience",
    "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": "Random graphs"
        },
        {
            "word": "hypergraphs"
        },
        {
            "word": "tight Hamilton cycles"
        },
        {
            "word": "resilience"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/2x43q0st",
    "frozenauthors": [
        {
            "first_name": "Peter",
            "middle_name": "",
            "last_name": "Allen",
            "name_suffix": "",
            "institution": "Department of Mathematics, London School of Economics, Houghton Street, London, WC2A 2AE, U.K.",
            "department": ""
        },
        {
            "first_name": "Olaf",
            "middle_name": "",
            "last_name": "Parczyk",
            "name_suffix": "",
            "institution": "Department of Mathematics and Computer Science, FU Berlin, Arnimallee 3, 14195 Berlin, Germany",
            "department": ""
        },
        {
            "first_name": "Vincent",
            "middle_name": "",
            "last_name": "Pfenninger",
            "name_suffix": "",
            "institution": "Institute of Discrete Mathematics, Graz University of Technology, Steyrergasse 30, 8010 Graz, Austria",
            "department": ""
        }
    ],
    "date_submitted": "2024-07-01T11:56:03+02:00",
    "date_accepted": "2024-07-01T11:56:03+02:00",
    "date_published": "2024-06-30T09:00:00+02:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64933/galley/49743/download/"
        }
    ]
}