Domatic number
（重定向自Domatic partition）
In graph theory, a domatic partition of a graph ![G = (V,E)](/Images/godic/202501/09/9e9992d6bf50b7580f971487c466a8cb0958.png")
is a partition of ![V](/Images/godic/202501/09/5206560a306a2e085a437fd258eb57ce0958.png")
into disjoint sets ![V_1](/Images/godic/202501/09/15df402d99d5ae494c0eec6b149b3dd90958.png")
, ![V_2](/Images/godic/202501/09/4925ee5356b4ace0e28f0324cf3a81de0958.png")
,...,![V_K](/Images/godic/202501/09/5752c1920921d5c194d6a1d9fb12d3f40958.png")
such that each Vi is a dominating set for G. The figure on the right shows a domatic partition of a graph; here the dominating set consists of the yellow vertices, consists of the green vertices, and ![V_3](/Images/godic/202501/09/12aff7a3dd429c727fb6b86474ab70e10958.png")
consists of the blue vertices.