Inapproximability of Maximum r-Regular Induced Connected Subgraph Problems*

摘要

Given a connected graph G = (V,E) on n vertices, the Maximum r-Regular Induced Connected Subgraph (r-MaxRICS) problem asks for a maximum sized subset of vertices 5 c V such that the induced subgraph GS on S is connected and r-regular. It is known that 2-MaxRICS and 3-MaxRICS are NP-hard. Moreover, 2-MaxRICS cannot be approximated within a factor of n1~ε in polynomial time for any ε> 0 unless P = NP. In this paper, we show that r-MaxRICS are NP-hard for any fixed integer r ≥ 4. Furthermore, we show that for any fixed integer r ≥ 3, r-MaxRICS cannot be approximated within a factor of nl/6~ε in polynomial time for any ε> 0 unless P = NP.