Domination Number of Graphs with Minimum Degree Five

Abstract

We prove that for every graph G on n vertices and with minimum degree five, the domination number γ(G) cannot exceed n/3. The proof combines an algorithmic approach and the discharging method. Using the same technique, we provide a shorter proof for the known upper bound 4n/11 on the domination number of graphs of minimum degree four.

Keywords

• dominating set
• domination number
• discharging method
• 05c69