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We consider the problem of developing algorithms for the recognition of a fixed pattern within a permutation. These methods are based upon using a carefully chosen chain or tree of subpatterns to build up the entire pattern. Generally, large improvements over brute force search can be obtained. Even using on-line versions of these methods provides such… (More)

We establish that if A is a set of at most 23 vertices in a 3-connected cubic planar graph G, then there is a cycle in G containing A. This result is sharp. Let G be a 3-connected cubic planar graph and let A ⊆ V (G). It was shown in [4] that if |A| ≤ 19 there is a cycle C in G such that A ⊆ V (C). In this paper we show that if |A| ≤ 23, then G contains a… (More)