On Rall's 1/2-conjecture on the domination game

Abstract

The 1/2-conjecture on the domination game asserts that if G is a traceable graph, then the game domination number _γg(G) of G is at most . A traceable graph is a 1/2-graph if _γg(G) = n(G)/2 holds. It is proved that the so-called hatted cycles are 1/2-graphs and that unicyclic graphs fulfill the 1/2-conjecture. Several additional families of graphs that support the conjecture are determined and computer experiments related to the conjecture described.