The 1/3-Conjectures for Domination in Cubic Graphs: Towards a Tighter Bound

This research paper disproves the long-held belief that the domination number of a cubic graph is ⌈n/3⌉ and explores two conjectures related to the domination number in cubic graphs, providing evidence for a tighter bound of γ(G) ≤ 1/3n under specific girth conditions.