A note on Haynes-Hedetniemi-Slater Conjecture

Abstract

We notice that Haynes-Hedetniemi-Slater Conjecture is true (i.e. $\gamma (G)\le \frac{\delta }{3\delta -1}n$ for every graph $G$ of size $n$ with minimum degree $\delta \ge 4$, where $\gamma (G)$ is the domination number of $G$). Because the conjecture for $\delta =6$ follows from the estimate n (1 - \prod_{i= 1}^[δ+ 1} (δi)/(δi + 1) by W. E. Clark, B. Shekhtman, S. Suen [Upper bounds of the Domination Number of a Graph, Congressus Numerantium, 132 (1998), pp. 99-123.]

2 pages