Article Instance

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

{
    "pk": 65047,
    "title": "Improved bound on the number of cycle sets",
    "subtitle": null,
    "abstract": "The cycle set of a graph \\(G\\) is the set consisting of all sizes of cycles in \\(G\\). Answering a conjecture of Erdős and Faudree, Verstraëte showed that there are at most \\(2^{n - n^{1/10}}\\) different cycle sets of graphs with \\(n\\) vertices. We improve this bound to \\(2^{n - n^{1/2 - o(1)}}\\). Our proof follows the general strategy of Verstraëte of reducing the problem to counting cycle sets of Hamiltonian graphs with many chords or a large maximum degree. The key new ingredients are near-optimal container lemmata for cycle sets of such graphs.\n \nMathematics Subject Classifications: 05C30, 05C38\n \nKeywords: Cycle sets, container method",
    "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": "Cycle sets"
        },
        {
            "word": "container method"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/4k75b3z7",
    "frozenauthors": [
        {
            "first_name": "Rajko",
            "middle_name": "",
            "last_name": "Nenadov",
            "name_suffix": "",
            "institution": "School of Computer Science, University of Auckland, Auckland, New Zealand",
            "department": ""
        }
    ],
    "date_submitted": "2026-04-20T13:01:20-07:00",
    "date_accepted": "2026-04-20T13:01:20-07:00",
    "date_published": "2026-04-20T00:00:00-07:00",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/65047/galley/49857/download/"
        }
    ]
}