TY  - JOUR
ID  - Chen2007
LB  - Chen2007
AU  - Chen, Xue-gang
TI  - Tree domatic number in graphs
ST  - Tree domatic number in graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2007
VL  - 27
IS  - 1
SP  - 5
EP  - 11
DO  - http://dx.doi.org/10.7494/OpMath.2007.27.1.5
UR  - http://dx.doi.org/10.7494/OpMath.2007.27.1.5
AB  - A dominating set \(S\) in a graph \(G\) is a tree dominating set of \(G\) if the subgraph induced by \(S\) is a tree. The tree domatic number of \(G\) is the maximum number of pairwise disjoint tree dominating sets in \(V(G)\). First, some exact values of and sharp bounds for the tree domatic number are given. Then, we establish a sharp lower bound for the number of edges in a connected graph of given order and given tree domatic number, and we characterize the extremal graphs. Finally, we show that a tree domatic number of a planar graph is at most \(4\) and give a characterization of planar graphs with the tree domatic number \(3\).
KW  - tree domatic number
KW  - regular graph
KW  - planar graph
KW  - Cartesian product
SN  - 1232-9274
ER  -