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A note on packing two copies of a tree into a graph with small maximum degree
Discrete Mathematics ( IF 0.7 ) Pub Date : 2020-10-01 , DOI: 10.1016/j.disc.2020.111991
Agnieszka Görlich , Mariusz Woźniak

Abstract Let T be a non-star tree of order n and maximum degree Δ . Hong Wang showed that there is a packing σ such that the degree of every vertex v in T ⊕ σ ( T ) does not exceed Δ ( T ) + 2 . In this note we improve this result in two directions. First, we show that with only one exception, there exists a packing σ such that Δ ( T ⊕ σ ( T ) ) ≤ Δ ( T ) + 1 . Moreover, this bound is, in a sense, uniform.

中文翻译:

关于将一棵树的两个副本打包成一个最大度数较小的图形的说明

摘要 设 T 为 n 阶最大度为 Δ 的非星型树。Hong Wang 证明存在一个包装 σ,使得 T ⊕ σ ( T ) 中每个顶点 v 的度数不超过 Δ ( T ) + 2 。在这篇笔记中,我们从两个方向改进了这个结果。首先,我们证明,除了一个例外,存在一个包装 σ,使得 Δ ( T ⊕ σ ( T ) ) ≤ Δ ( T ) + 1 。而且,这个界限在某种意义上是一致的。
更新日期:2020-10-01
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