Article Instance

HTTP 200 OK
Allow: GET
Content-Type: application/json
Vary: Accept

{
    "pk": 64808,
    "title": "Large hypergraphs without tight cycles",
    "subtitle": null,
    "abstract": "An $r$-uniform tight cycle of length $\\ell>r$ is a hypergraph with vertices $v_1,\\dots,v_\\ell$ and edges $\\{v_i,v_{i+1},\\dots,v_{i+r-1}\\}$ (for all $i$), with the indices taken modulo $\\ell$. It was shown by Sudakov and Tomon that for each fixed $r\\geq 3$, an $r$-uniform hypergraph on $n$ vertices which does not contain a tight cycle of any length has at most $n^{r-1+o(1)}$ hyperedges, but the best known construction (with the largest number of edges) only gives $\\Omega(n^{r-1})$ edges. In this note we prove that, for each fixed $r\\geq 3$, there are $r$-uniform hypergraphs with $\\Omega(n^{r-1}\\log n/\\log\\log n)$ edges which contain no tight cycles, showing that the $o(1)$ term in the exponent of the upper bound is necessary.\nMathematics Subject Classifications: 05C65, 05C38",
    "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": [],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/7hk9r04f",
    "frozenauthors": [
        {
            "first_name": "Barnabás",
            "middle_name": "",
            "last_name": "Janzer",
            "name_suffix": "",
            "institution": "Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge, United Kingdom",
            "department": ""
        }
    ],
    "date_submitted": "2021-11-12T15:54:22Z",
    "date_accepted": "2021-11-12T15:54:22Z",
    "date_published": "2021-12-15T08:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64808/galley/49618/download/"
        }
    ]
}