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ARSCOM
2004

The Domatic Number of Regular Graphs

13 years 10 months ago
The Domatic Number of Regular Graphs
The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular graph is almost surely at most r, and that for 3-regular random graphs, the domatic number is almost surely equal to 3. We also give a lower bound on the domatic number of a graph in terms of order, minimum degree and maximum degree. As a corollary, we obtain the result that the domatic number of an r-regular graph is at least (r + 1)/(3ln(r + 1)).
Peter Dankelmann, Neil J. Calkin
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2004
Where ARSCOM
Authors Peter Dankelmann, Neil J. Calkin
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