TY - JOUR
T1 - The domination number of the graph defined by two levels of the n-cube, II
AU - Balogh, József
AU - Katona, Gyula O.H.
AU - Linz, William
AU - Tuza, Zsolt
N1 - Publisher Copyright:
© 2020 The Authors
PY - 2021/1
Y1 - 2021/1
N2 - 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].
AB - 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].
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U2 - 10.1016/j.ejc.2020.103201
DO - 10.1016/j.ejc.2020.103201
M3 - Article
AN - SCOPUS:85089457304
SN - 0195-6698
VL - 91
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
M1 - 103201
ER -