On a conjecture on total domination in claw-free cubic graphs: proof and new upper bound.

Abstract

In 2008, Favaron and Henning proved that if G is a connected claw-free cubic graph of order n ≥ 10, then the total domination number γt(G)ofG is at most 5 11n, and they conjectured that in fact γt(G) isatmost4n (see 9