Abstract

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→R+, a vertex set C⊆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)≡1,v∈V, which are denoted as MinkBDND and MinCkBDND. This paper presents a (1+ε) and a 3.76-approximation algorithm for MinkBDND and MinCkBDND on unit disk graphs, respectively, where 0<ε<1 is an arbitrary constant.

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