Abstract
Bryant et al. (2014) propose a graph cleaning process and study the corresponding brush number. As their main result they show that the brush number of a tree with ℓ leaves is at least ⌊ℓ+12⌋ and at most ⌈ℓ+12⌉. Answering one of their questions, we show that the trees with an even number ℓ of leaves and brush number ℓ2 can be recognized efficiently. Furthermore, we provide a simpler proof of their main result.
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