The $k$-domatic number of a graph

Kämmerling, Karsten, and Volkmann, Lutz. "The $k$-domatic number of a graph." Czechoslovak Mathematical Journal 59.2 (2009): 539-550. <http://eudml.org/doc/37939>.

@article{Kämmerling2009,
abstract = {Let $k$ be a positive integer, and let $G$ be a simple graph with vertex set $V(G)$. A $k$-dominating set of the graph $G$ is a subset $D$ of $V(G)$ such that every vertex of $V(G)-D$ is adjacent to at least $k$ vertices in $D$. A $k$-domatic partition of $G$ is a partition of $V(G)$ into $k$-dominating sets. The maximum number of dominating sets in a $k$-domatic partition of $G$ is called the $k$-domatic number$d_k(G)$. In this paper, we present upper and lower bounds for the $k$-domatic number, and we establish Nordhaus-Gaddum-type results. Some of our results extend those for the classical domatic number $d(G)=d_1(G)$.},
author = {Kämmerling, Karsten, Volkmann, Lutz},
journal = {Czechoslovak Mathematical Journal},
keywords = {domination; $k$-domination; $k$-domatic number; domination; -domination; -domatic number; vertex partition; Nordhaus-Gaddum type results},
language = {eng},
number = {2},
pages = {539-550},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The $k$-domatic number of a graph},
url = {http://eudml.org/doc/37939},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Kämmerling, Karsten
AU - Volkmann, Lutz
TI - The $k$-domatic number of a graph
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 539
EP - 550
AB - Let $k$ be a positive integer, and let $G$ be a simple graph with vertex set $V(G)$. A $k$-dominating set of the graph $G$ is a subset $D$ of $V(G)$ such that every vertex of $V(G)-D$ is adjacent to at least $k$ vertices in $D$. A $k$-domatic partition of $G$ is a partition of $V(G)$ into $k$-dominating sets. The maximum number of dominating sets in a $k$-domatic partition of $G$ is called the $k$-domatic number$d_k(G)$. In this paper, we present upper and lower bounds for the $k$-domatic number, and we establish Nordhaus-Gaddum-type results. Some of our results extend those for the classical domatic number $d(G)=d_1(G)$.
LA - eng
KW - domination; $k$-domination; $k$-domatic number; domination; -domination; -domatic number; vertex partition; Nordhaus-Gaddum type results
UR - http://eudml.org/doc/37939
ER -