English

A note on Haynes-Hedetniemi-Slater Conjecture

Group Theory 2010-11-16 v1

Abstract

We notice that Haynes-Hedetniemi-Slater Conjecture is true (i.e. γ(G)δ3δ1n\gamma(G) \leq \frac{\delta}{3\delta -1}n for every graph GG of size nn with minimum degree δ4\delta \geq 4, where γ(G)\gamma(G) is the domination number of GG). Because the conjecture for δ=6\delta =6 follows from the estimate n (1 - \prod_{i= 1}^[\delta + 1} (\delta i)/(\delta i + 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.]

Keywords

Cite

@article{arxiv.1011.3383,
  title  = {A note on Haynes-Hedetniemi-Slater Conjecture},
  author = {Tomoo Yokoyama},
  journal= {arXiv preprint arXiv:1011.3383},
  year   = {2010}
}

Comments

2 pages

R2 v1 2026-06-21T16:43:53.991Z