Research Article

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

Published in: Quaestiones Mathematicae
Volume 44 , issue 12 , 2021 , pages: 1711–1727

DOI: 10.2989/16073606.2020.1822945

Author(s): Csilla Bujtás , Slovenia , Vesna Iršič , Slovenia , Sandi Klavžar , Slovenia , Kexiang Xu , P.R. China

Keywords: 05C57 , 05C69 , 91A43 , 05C57 , 05C69 , 91A43

Abstract

The 1/2-conjecture on the domination game asserts that if G is a traceable graph, then the game domination number γ_g (G) of G is at most A traceable graph is a 1/2-graph if 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.

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