Consider all k-element subsets and ℓ-element subsets (k>ℓ) of an n-element set as vertices of a bipartite graph. Two vertices are adjacent if the corresponding ℓ-element set is a subset of the corresponding k-element set. Let Gk,ℓ denote this graph. The domination number of Gk,1 was exactly determined by Badakhshian, Katona and Tuza. A conjecture was also stated there on the asymptotic value (n tending to infinity) of the domination number of Gk,2. Here we prove the conjecture, determining the asymptotic value of the domination number [Formula presented].
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics