Domination and Total Domination in Hypergraphs

Michael A. Henning, Anders Yeo

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


A dominating set in a hypergraph H with vertex set V (H) and E(H) is a subset of vertices D ⊆ V (H) such that for every vertex v ∈ V (H) ∖ D, there exists an edge e ∈ E(H) for which v ∈ e and e ∩ D≠∅. A total dominating set in H is a dominating set D of H with the additional property that for every vertex v in D, there exists an edge e ∈ E(H) for which v ∈ e and e ∩ (D ∖{v})≠∅. The domination number γ(H) and the total domination number γt(H) are the minimum cardinalities of a dominating set and total dominating set, respectively, in H. This chapter presents an overview of research on domination and total domination in hypergraphs.

Original languageEnglish
Title of host publicationDevelopments in Mathematics
Number of pages29
Publication statusPublished - 2021

Publication series

NameDevelopments in Mathematics
ISSN (Print)1389-2177
ISSN (Electronic)2197-795X


  • Dominating set
  • Hypergraph domination
  • Total dominating set

ASJC Scopus subject areas

  • General Mathematics


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