Connected domatic number in planar graphs

@article{Hartnell2001,
abstract = {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.},
author = {Hartnell, Bert L., Rall, Douglas F.},
journal = {Czechoslovak Mathematical Journal},
keywords = {connected dominating set; connected domatic number; planar; connected dominating set; connected domatic number; planar},
language = {eng},
number = {1},
pages = {173-179},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Connected domatic number in planar graphs},
url = {http://eudml.org/doc/30624},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Hartnell, Bert L.
AU - Rall, Douglas F.
TI - Connected domatic number in planar graphs
JO - Czechoslovak Mathematical Journal
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 1
SP - 173
EP - 179
AB - 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.
LA - eng
KW - connected dominating set; connected domatic number; planar; connected dominating set; connected domatic number; planar
UR - http://eudml.org/doc/30624
ER -