edge-domatic number; cactus; dominating; edge-domatic partition; round; round cactus
The edge-domatic number of a graph is the maximum number of classes of a partition of its edge set into dominating sets. This number is studied for cacti, i.e. graphs in which each edge belongs to at most one circuit.
 B. Zelinka: Edge-domatic number of a graph
. Czechoslovak Math. J. 33 (198З), 107-110. MR 0687422