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.

中文翻译：

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关于拉尔关于统治博弈的 1/2 猜想

摘要

支配博弈的 1/2 猜想断言，如果G是一个可溯图，那么G的博弈支配数γ _g ( G )至多是一个可溯图，如果成立，则为 1/2-图。证明了所谓的帽子循环是1/2-图，而单环图满足1/2-猜想。确定了支持该猜想的几个附加图族，并描述了与该猜想相关的计算机实验。