Dominating cliques in graphs

Margaret B. Cozzens; Laura L. Kelleher

doi:10.1016/0012-365X(90)90353-J

Dominating cliques in graphs

Margaret B. Cozzens
, Laura L. Kelleher

Research output: Contribution to journal › Article › peer-review

58 Scopus citations

Abstract

A set of vertices is a dominating set in a graph if every vertex not in the dominating set is adjacent to one or more vertices in the dominating set. A dominating clique is a dominating set that induces a complete subgraph. Forbidden subgraph conditions sufficient to imply the existence of a dominating clique are given. For certain classes of graphs, a polynomial algorithm is given for finding a dominating clique. A forbidden subgraph characterization is given for a class of graphs that have a connected dominating set of size three.

Original language	English (US)
Pages (from-to)	101-116
Number of pages	16
Journal	Discrete Mathematics
Volume	86
Issue number	1-3
DOIs	https://doi.org/10.1016/0012-365X(90)90353-J
State	Published - Dec 14 1990
Externally published	Yes

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(90)90353-J

Cite this

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abstract = "A set of vertices is a dominating set in a graph if every vertex not in the dominating set is adjacent to one or more vertices in the dominating set. A dominating clique is a dominating set that induces a complete subgraph. Forbidden subgraph conditions sufficient to imply the existence of a dominating clique are given. For certain classes of graphs, a polynomial algorithm is given for finding a dominating clique. A forbidden subgraph characterization is given for a class of graphs that have a connected dominating set of size three.",

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AB - A set of vertices is a dominating set in a graph if every vertex not in the dominating set is adjacent to one or more vertices in the dominating set. A dominating clique is a dominating set that induces a complete subgraph. Forbidden subgraph conditions sufficient to imply the existence of a dominating clique are given. For certain classes of graphs, a polynomial algorithm is given for finding a dominating clique. A forbidden subgraph characterization is given for a class of graphs that have a connected dominating set of size three.

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Dominating cliques in graphs

Abstract

All Science Journal Classification (ASJC) codes

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