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Asymptotic bounds on total domination in regular graphs
Discrete Mathematics ( IF 0.8 ) Pub Date : 2021-01-14 , DOI: 10.1016/j.disc.2020.112287
Carlos Hoppen , Giovane Mansan

We obtain new upper bounds on the size of a minimum total dominating set for random regular graphs and for regular graphs with large girth. In particular, they imply that an upper bound conjectured by Thomassé and Yeo (2007) holds asymptotically almost surely for 5-regular graphs and holds for all 5-regular graphs with sufficiently large girth. Our bounds are obtained through the analysis of a local algorithm using a method due to Hoppen and Wormald (2018).



中文翻译:

正则图中总控制的渐近界

对于随机正则图和大周长的正则图,我们获得了最小总控制集大小的新上限。特别是,它们暗示着Thomassé和Yeo(2007)猜想的一个上界对于5正则图几乎可以肯定地成立,而对所有周长足够大的5正则图都成立。我们的边界是通过使用Hoppen和Wormald(2018)提出的方法对局部算法进行分析而获得的。

更新日期:2021-01-14
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