@inbook{6a1a787994584c5591bca26ccf3b364f,

title = "Domination and Total Domination in Hypergraphs",

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.",

keywords = "Dominating set, Hypergraph domination, Total dominating set",

author = "Henning, {Michael A.} and Anders Yeo",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2021",

doi = "10.1007/978-3-030-58892-2_11",

language = "English",

series = "Developments in Mathematics",

publisher = "Springer",

pages = "311--339",

booktitle = "Developments in Mathematics",

address = "Germany",

}