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{
    "pk": 64825,
    "title": "On the homology of independence complexes",
    "subtitle": null,
    "abstract": "The independence complex $\\mathrm{Ind}(G)$ of a graph $G$ is the simplicial complex formed by its independent sets of vertices. We introduce a deformation of the simplicial chain complex of $\\mathrm{Ind}(G)$ that gives rise to a spectral sequence which contains on its first page the homology groups of the independence complexes of $G$ and various subgraphs of $G$, obtained by removing independent sets together with their neighborhoods. We show how this can be used to study the homology of $\\mathrm{Ind}(G)$. Furthermore, a careful investigation of the sequence's first page exhibits a relation between the cardinality of maximal independent sets in $G$ and the vanishing of certain homology groups of independence complexes of subgraphs of $G$. We show that it holds for all paths and cycles.\n \nMathematics Subject Classifications: 05C69, 55U10",
    "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": "Graph"
        },
        {
            "word": "independent set"
        },
        {
            "word": "independence complex"
        },
        {
            "word": "homology groups"
        }
    ],
    "section": "Research Articles",
    "is_remote": true,
    "remote_url": "https://escholarship.org/uc/item/9r20x01z",
    "frozenauthors": [
        {
            "first_name": "Marko",
            "middle_name": "",
            "last_name": "Berghoff",
            "name_suffix": "",
            "institution": "Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany",
            "department": ""
        }
    ],
    "date_submitted": "2022-03-23T20:11:03Z",
    "date_accepted": "2022-03-23T20:11:03Z",
    "date_published": "2022-03-31T07:00:00Z",
    "render_galley": null,
    "galleys": [
        {
            "label": "",
            "type": "pdf",
            "path": "https://journalpub.escholarship.org/combinatorial_theory/article/64825/galley/49635/download/"
        }
    ]
}