The Subgraph Isomorphism Problem for Outerplanar Graphs

This paper deals with the: subgraph isomorphism problem for outerplanar graphs (SUBOUTISOM). In general, since trees and forests are outerplanar, SUBOUTISOM is NPcomplete. We show that SUBOUTISOM remains NP-complete even when the strongest connectivity requirements are imposed on both graphs. The same result holds for the induced subgraph isomorphism problem for outerplanar graphs except the case when both graphs arc 2-connected; for such graphs we give a palynomial algorithm which verifies whether a 2-connectea outerplanar graph is an induced subgraph of another 2-connected outerplanar gralph.