1. Connected domatic number in planar graphs
- Creator:
- Hartnell, Bert L. and Rall, Douglas F.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- connected dominating set, connected domatic number, and planar
- Language:
- English
- Description:
- A dominating set in a graph $G$ is a connected dominating set of $G$ if it induces a connected subgraph of $G$. The connected domatic number of $G$ is the maximum number of pairwise disjoint, connected dominating sets in $V(G)$. We establish a sharp lower bound on the number of edges in a connected graph with a given order and given connected domatic number. We also show that a planar graph has connected domatic number at most 4 and give a characterization of planar graphs having connected domatic number 3.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public