1 Ocak 2020 Dergi makalesi Açık Erişim

Ekinci, Gulnaz Boruzanli; Bujtas, Csilla

Citation Style Language JSON

{
  "DOI": "10.1515/math-2020-0047", 
  "abstract": "Let k be a positive integer and let G be a graph with vertex set V(G). A subset D subset of V(G) is a k-dominating set if every vertex outside D is adjacent to at least k vertices in D. The k-domination number gamma(k)(G) is the minimum cardinality of a k-dominating set in G. For any graph G, we know that gamma(k)(G) >= gamma(G) + k - 2 where Delta(G) >= k >= 2 and this bound is sharp for every k >= 2. In this paper, we characterize bipartite graphs satisfying the equality for k >= 3 and present a necessary and sufficient condition for a bipartite graph to satisfy the equality hereditarily when k = 3. We also prove that the problem of deciding whether a graph satisfies the given equality is NP-hard in general.", 
  "author": [
    {
      "family": "Ekinci", 
      "given": " Gulnaz Boruzanli"
    }, 
    {
      "family": "Bujtas", 
      "given": " Csilla"
    }
  ], 
  "container_title": "OPEN MATHEMATICS", 
  "id": "4761", 
  "issued": {
    "date-parts": [
      [
        2020, 
        1, 
        1
      ]
    ]
  }, 
  "page": "873-885", 
  "title": "Bipartite graphs with close domination and k-domination numbers", 
  "type": "article-journal", 
  "volume": "18"
}