The domination number of the graph defined by two levels of the n-cube

Leila Badakhshian, Gyula O.H. Katona, Z. Tuza

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Abstract

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 G k,ℓ denote this graph The domination number of G k,1 will exactly be determined. We also give lower and upper estimates on the domination number G k,2 and pose a conjecture of asymptotic nature.

Original languageEnglish
JournalDiscrete Applied Mathematics
DOIs
Publication statusPublished - Jan 1 2019

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Keywords

  • Domination number
  • Transversal design
  • Turán theorem

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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