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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.
[1] E. J. Cockayne S. T. Hedetniemi: Towards a theory of domination in graphs. Networks 7 (1977), 247-261. DOI 10.1002/net.3230070305 | MR 0483788
[2] B. Zelinka: Edge-domatic number of a graph. Czechoslovak Math. J. 33 (198З), 107-110. MR 0687422
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