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 language | English |
|---|---|
| Title of host publication | Structures of Domination in Graphs |
| Editors | Michael A. Henning, Anders Yeo |
| Publisher | Springer |
| Publication date | 2021 |
| Pages | 311-339 |
| ISBN (Print) | 978-3-030-58891-5 |
| ISBN (Electronic) | 978-3-030-58892-2 |
| DOIs | |
| Publication status | Published - 2021 |
| Series | Developments in Mathematics |
|---|---|
| Volume | 66 |
| ISSN | 1389-2177 |
Bibliographical note
Publisher Copyright:© 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Keywords
- Dominating set
- Hypergraph domination
- Total dominating set