Essec\Faculty\Model\Contribution {#2233
  #_index: "academ_contributions"
  #_id: "16236"
  #_source: array:26 [
    "id" => "16236"
    "slug" => "16236-the-1-persistency-of-the-clique-relaxation-of-the-stable-set-polytope-a-focus-on-some-forbidden-structures"
    "yearMonth" => "2026-07"
    "year" => "2026"
    "title" => "The 1-persistency of the clique relaxation of the stable set polytope: A focus on some forbidden structures"
    "description" => "DELLE DONNE, D., ESCALANTE, M., FEKETE, P. et MORONI, L. (2026). The 1-persistency of the clique relaxation of the stable set polytope: A focus on some forbidden structures. <i>Discrete Applied Mathematics</i>, 387(1), pp. 37-56."
    "authors" => array:4 [
      0 => array:3 [
        "name" => "DELLE DONNE Diego"
        "bid" => "B00788133"
        "slug" => "delle-donne-diego"
      ]
      1 => array:1 [
        "name" => "Escalante M."
      ]
      2 => array:1 [
        "name" => "Fekete P."
      ]
      3 => array:1 [
        "name" => "Moroni L."
      ]
    ]
    "ouvrage" => ""
    "keywords" => array:3 [
      0 => "Stable set polytope"
      1 => "Persistency"
      2 => "Integer programming"
    ]
    "updatedAt" => "2026-03-03 14:54:51"
    "publicationUrl" => "https://doi.org/10.1016/j.dam.2026.02.033"
    "publicationInfo" => array:3 [
      "pages" => "37-56"
      "volume" => "387"
      "number" => "1"
    ]
    "type" => array:2 [
      "fr" => "Articles"
      "en" => "Journal articles"
    ]
    "support_type" => array:2 [
      "fr" => "Revue scientifique"
      "en" => "Scientific journal"
    ]
    "countries" => array:2 [
      "fr" => null
      "en" => null
    ]
    "abstract" => array:2 [
      "fr" => ""
      "en" => """
        A polytope PPP is said to have the persistency property if for every vector ccc and every LPLPLP-optimal point x∗x^*x∗, there exists a IPIPIP-optimal integer point xxx such that xi=xi∗x_i = x^*_ixi​=xi∗​ for each iii with xi∗x^*_ixi∗​ integer.\n
        In this paper, we consider a relaxation of the persistency property called 1-persistency. We study the family F\mathcal{F}F of graphs whose clique relaxation of the stable set polytope has 1-persistency, and we refer to them as F\mathcal{F}F-persistent graphs. We provide sufficient conditions for a graph to be F\mathcal{F}F-persistent, and identify several graph classes of this family. Motivated by a necessary condition of this property, we introduce the family of kkk-umbrella graphs, and study which of them belong to F\mathcal{F}F. The property of being F\mathcal{F}F-persistent is a hereditary property for graphs, and then it becomes relevant to study the minimal forbidden structures for the family F\mathcal{F}F, i.e., minimally not F\mathcal{F}F-persistent (mnF\mathcal{F}F) graphs. In this line, we identify some mnF\mathcal{F}F-umbrella graphs and also other forbidden minimal structures for F\mathcal{F}F-persistency outside this family (named as whale graphs).
        """
    ]
    "authors_fields" => array:2 [
      "fr" => "Systèmes d'Information, Data Analytics et Opérations"
      "en" => "Information Systems, Data Analytics and Operations"
    ]
    "indexedAt" => "2026-03-13T18:21:44.000Z"
    "docTitle" => "The 1-persistency of the clique relaxation of the stable set polytope: A focus on some forbidden structures"
    "docSurtitle" => "Articles"
    "authorNames" => "<a href="/cv/delle-donne-diego">DELLE DONNE Diego</a>, Escalante M., Fekete P., Moroni L."
    "docDescription" => "<span class="document-property-authors">DELLE DONNE Diego, Escalante M., Fekete P., Moroni L.</span><br><span class="document-property-authors_fields">Systèmes d'Information, Data Analytics et Opérations</span> | <span class="document-property-year">2026</span>"
    "keywordList" => "<a href="#">Stable set polytope</a>, <a href="#">Persistency</a>, <a href="#">Integer programming</a>"
    "docPreview" => "<b>The 1-persistency of the clique relaxation of the stable set polytope: A focus on some forbidden structures</b><br><span>2026-07 | Articles </span>"
    "docType" => "research"
    "publicationLink" => "<a href="https://doi.org/10.1016/j.dam.2026.02.033" target="_blank">The 1-persistency of the clique relaxation of the stable set polytope: A focus on some forbidden structures</a>"
  ]
  +lang: "fr"
  +"_score": 8.674812
  +"_ignored": array:1 [
    0 => "abstract.en.keyword"
  ]
  +"parent": null
}