Testing whether a digraph contains H-free k-induced subgraphs

Authors:
Hong-Yiu Lin;Yuh-Dauh Lyuu;Tak-Man Ma;Yen-Wu Ti
Affiliations:
Department of Computer Science and Information Engineering, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan;Department of Computer Science and Information Engineering, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan;MediaTek Inc., Hsinchu, Taiwan;Department of Computer Science and Information Engineering, National Taiwan University, No.1, Sec. 4, Roosevelt Road, Taipei 106, Taiwan
Venue:
Theoretical Computer Science
Year:
2008

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Abstract

A subgraph induced by k vertices is called a k-induced subgraph. We prove that determining if a digraph G contains H-free k-induced subgraphs is @W(N^2)-evasive. Then we construct an @e-tester to test this property. (An @e-tester for a property @P is guaranteed to distinguish, with probability at least 2/3, between the case of G satisfying @P and the case of G being @e-far from satisfying @P.) The query complexity of the @e-tester is independent of the size of the input digraph. An (@e,@d)-tester for a property @P is an @e-tester for @P that is furthermore guaranteed to accept with probability at least 2/3 any input that is @d-close to satisfying @P. This paper presents an (@e,@d)-tester for whether a digraph contains H-free k-induced subgraphs.