ARSCOM
2004
13 years 10 months ago
2004
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 g...
MST
2006
13 years 10 months ago
2006
We prove that the exact versions of the domatic number problem are complete for the levels of the boolean hierarchy over NP. The domatic number problem, which arises in the area of...
FOCS
2006
IEEE
14 years 5 months ago
2006
IEEE
Given an n-element set U and a family of subsets S ⊆ 2U we show how to count the number of k-partitions S1 ∪ · · · ∪ Sk = U into subsets Si ∈ S in time 2nnO(1). The only...