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Let G be a 3-connected planar graph and let U ı V(G). It is shown that G contains a K 2, t minor such that t is large and each vertex of degree 2 in K 2, t corresponds to some vertex of U if and only if there is no small face cover of U. This result cannot be extended to 2-connected planar graphs. © 2002 Elsevier Science (USA)doi:10.1006/jctb.2001.2083 fatcat:tlki2yzit5e3fnhwaedn75mwl4