无爪图的可约干少叶生成树

Pub Date : 2021-12-08 DOI:10.1556/012.2023.01538

P. Ha

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引用次数: 2

摘要

让我成为一棵树。T的可约干是包含T的所有分支顶点的最小子树。本文首先利用Gould和Shull[5]的新技术，在无爪图的有界叶生成树上对Kano等人[10]的结果给出了一个新的简短证明。然后，我们用类似的思想证明了一个无爪图的一个尖锐的充分条件，该无爪图具有一个生成树，其可约茎有几个叶。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Spanning Trees of a Claw-Free Graph Whose Reducible Stems Have Few Leaves

Let T be a tree. The reducible stem of T is the smallest subtree that contains all branch vertices of T. In this paper, we first use a new technique of Gould and Shull [5] to state a new short proof for a result of Kano et al. [10] on the spanning tree with a bounded number of leaves in a claw-free graph. After that, we use a similar idea to prove a sharp sufficient condition for a claw-free graph having a spanning tree whose reducible stem has few leaves.

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