论文标题
界定K-Rainbow总统治数
Bounding the k-rainbow total domination number
论文作者
论文摘要
最近，针对图形$ g $引入了$ k $ rainbow总统治的概念，这是出于渴望减少$ g $上的整数标记问题的总体统治数量的渴望。在本文中，我们进一步证明了标签方法的有用性，以总统治数，彩虹统治数量和彩虹总统治数以及通常的统治数来呈现彩虹总统治数量的界限，后者列出了Goddard and Henning（2018）的结果。我们为彩虹统治和彩虹总统治建立了鲜明的结果。通过说明彩虹总统治的敏锐的猜想，我们在两部分图的情况下对Viping的原始猜想提出了不同的观点。
Recently the notion of $k$-rainbow total domination was introduced for a graph $G$, motivated by a desire to reduce the problem of computing the total domination number of the generalized prism $G \Box K_k$ to an integer labeling problem on $G$. In this paper we further demonstrate usefulness of the labeling approach, presenting bounds on the rainbow total domination number in terms of the total domination number, the rainbow domination number and the rainbow total domination number, as well as the usual domination number, where the latter presents a generalization of a result by Goddard and Henning (2018). We establish Vizing-like results for rainbow domination and rainbow total domination. By stating a Vizing-like conjecture for rainbow total domination we present a different viewpoint on Vizing's original conjecture in the case of bipartite graphs.
