In this paper, we study the minimum (connected) k-bounded-degree node deletion problem (Min(C)kBDND). For a connected graph G, a constant k and a weight function $w:V\to {\mathbb{R}}^{+}$, a vertex set $C\subseteq V(G)$ is a kBDND-set if the maximum degree of graph $G-C$ is at most k. If furthermore, the subgraph of G induced by C is connected, then C is a CkBDND-set. The goal of MinWkBDND (resp. MinWCkBDND) is to find a kBDND-set (resp. CkBDND-set) with the minimum weight. In this paper, we focus on their cardinality versions with $w(v)\equiv 1,v\in V$, which are denoted as MinkBDND and MinCkBDND. This paper presents a $(1+\epsilon )$ and a 3.76-approximation algorithm for MinkBDND and MinCkBDND on unit disk graphs, respectively, where $0<\epsilon <1$ is an arbitrary constant.

在本文中，我们研究了最小（连通）k界度节点删除问题（Min（C）k BDND）。对于连通图G，常数k和权函数$w：V\to {\mathbb{[R}}^{+}$，顶点集 $C\subseteq V（G）$如果最大图度是k BDND集$G-C$最多为k。此外，如果连接由C诱导的G的子图，则C是C k BDND集。MinW k BDND（分别为MinWC k BDND）的目标是找到一个权重最小的k BDND集（分别为C k BDND集）。在本文中，我们重点介绍了它们的基数版本$w（v）\equiv \mathrm{1个}，v\in V$，分别表示为Min k BDND和MinC k BDND。本文提出了一个$（\mathrm{1个}+\epsilon ）$以及分别在单位圆图上针对Min k BDND和MinC k BDND的3.76近似算法，其中$0<\epsilon <\mathrm{1个}$ 是一个任意常数。