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{
    "pk": 64934,
    "title": "The spectral even cycle problem",
    "subtitle": null,
    "abstract": "In this paper, we study the maximum adjacency spectral radii of graphs of large order that do not contain an even cycle of given length. For \\(n›k\\), let \\(S_{n,k}\\) be the join of a clique on \\(k\\) vertices with an independent set of \\(n-k\\) vertices and denote by \\(S_{n,k}^+\\) the graph obtained from \\(S_{n,k}\\) by adding one edge. In 2010, Nikiforov conjectured that for \\(n\\) large enough, the \\(C_{2k+2}\\)-free graph of maximum spectral radius is \\(S_{n,k}^+\\) and that the \\(\\{C_{2k+1},C_{2k+2}\\}\\)-free graph of maximum spectral radius is \\(S_{n,k}\\). We solve this two-part conjecture.\n \nMathematics Subject Classifications: 05C35, 05C50\n \nKeywords: Spectral Turán number, even-cycle problem, Brualdi-Solheid problem",
    "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": "Spectral Turán number"
        },
        {
            "word": "even-cycle problem"
        },
        {
            "word": "Brualdi-Solheid problem"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/64r017cx",
    "frozenauthors": [
        {
            "first_name": "Sebastian",
            "middle_name": "",
            "last_name": "Cioab",
            "name_suffix": "",
            "institution": "Department of Mathematical Sciences, University of Delaware, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Dheer",
            "middle_name": "Noal",
            "last_name": "Desai",
            "name_suffix": "",
            "institution": "Department of Mathematical Sciences, University of Memphis, U.S.A.",
            "department": ""
        },
        {
            "first_name": "Michael",
            "middle_name": "",
            "last_name": "Tait",
            "name_suffix": "",
            "institution": "Department of Mathematics & Statistics, Villanova University, U.S.A.",
            "department": ""
        }
    ],
    "date_submitted": "2024-07-01T15:26:42+02:00",
    "date_accepted": "2024-07-01T15:26:42+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/64934/galley/49744/download/"
        }
    ]
}