Domination and Total Domination in Hypergraphs

Michael A. Henning, Anders Yeo*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review

Abstract

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 publicationStructures of Domination in Graphs
EditorsMichael A. Henning, Anders Yeo
PublisherSpringer
Publication date2021
Pages311-339
ISBN (Print)978-3-030-58891-5
ISBN (Electronic)978-3-030-58892-2
DOIs
Publication statusPublished - 2021
SeriesDevelopments in Mathematics
Volume66
ISSN1389-2177

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

  • Dominating set
  • Hypergraph domination
  • Total dominating set

Fingerprint

Dive into the research topics of 'Domination and Total Domination in Hypergraphs'. Together they form a unique fingerprint.

Cite this