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{
    "pk": 64871,
    "title": "Disjoint dijoins for classes of dicuts in finite and infinite digraphs",
    "subtitle": null,
    "abstract": "A dicut in a directed graph is a cut for which all of its edges are directed to a common side of the cut. A famous theorem of Lucchesi and Younger states that in every finite digraph the least size of a set of edges meeting every non-empty dicut equals the maximum number of disjoint dicuts in that digraph. Such sets are called dijoins. Woodall conjectured a dual statement. He asked whether the maximum number of disjoint dijoins in a directed graph equals the minimum size of a non-empty dicut. We study a modification of this question where we restrict our attention to certain classes of non-empty dicuts, i.e. whether for a class \\(\\mathfrak{B}\\) of dicuts of a directed graph the maximum number of disjoint sets of edges meeting every dicut in \\(\\mathfrak{B}\\) equals the size of a minimum dicut in \\(\\mathfrak{B}\\). In particular, we verify this questions for nested classes of finite dicuts, for the class of dicuts of minimum size, and for classes of infinite dibonds, and we investigate how this generalised setting relates to a capacitated version of this question.\n \nMathematics Subject Classifications: 05C20, 05C70 (primary); 05C65, 05C63 (secondary)\n \nKeywords: Woodall's conjecture, digraphs, directed cuts, dijoins, dijoin packing",
    "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": "Woodall's conjecture"
        },
        {
            "word": "digraphs"
        },
        {
            "word": "directed cuts"
        },
        {
            "word": "dijoins"
        },
        {
            "word": "dijoin packing"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/8cz6n02x",
    "frozenauthors": [
        {
            "first_name": "J.",
            "middle_name": "Pascal",
            "last_name": "Gollin",
            "name_suffix": "",
            "institution": "Discrete Mathematics Group, Institute for Basic Science, Daejeon, Republic of Korea",
            "department": ""
        },
        {
            "first_name": "Karl",
            "middle_name": "",
            "last_name": "Heuer",
            "name_suffix": "",
            "institution": "Department of Applied Mathematics and Computer Science, Technical University of Denmark, Kongens Lyngby, Denmark",
            "department": ""
        },
        {
            "first_name": "Konstantinos",
            "middle_name": "",
            "last_name": "Stavropoulos",
            "name_suffix": "",
            "institution": "Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany",
            "department": ""
        }
    ],
    "date_submitted": "2022-10-13T06:37:18Z",
    "date_accepted": "2022-10-13T06:37:18Z",
    "date_published": "2022-10-15T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64871/galley/49681/download/"
        }
    ]
}