Inapproximability of Maximum r-Regular Induced Connected Subgraph Problems

Yuichi ASAHIRO, Hiroshi ETO, Eiji MIYANO
2013 IEICE transactions on information and systems  
Given a graph G = (V, E) on n vertices, the MAXIMUM r-REGULAR INDUCED CONNECTED SUB-GRAPH (r-MaxRICS) problems ask for a maximum sized subset of vertices S ⊆ V such that the induced subgraph G[S] on S is connected and r-regular. For r = 2, it is known that 2-MaxRICS is N P-hard and cannot be approximated within a factor of n 1−ε in polynomial time for any ε > 0 if P = N P. In this paper, we show that r-MaxRICS is N P-hard for any fixed integer r ≥ 3, and furthermore r-MaxRICS cannot be
more » ... cannot be approximated within a factor of n 1/6−ε in polynomial time for any ε > 0 if P = N P.
doi:10.1587/transinf.e96.d.443 fatcat:axlfs7arvrb2jl3tu247qbhsui