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We show that every quadrangulation of the sphere can be transformed into a 4-cycle by deletions of degree-2 vertices and by t-contractions at degree-3 vertices. A t-contraction simultaneously contracts all incident edges at a vertex with stable neighbourhood. The operation is mainly used in the field of t-perfect graphs. We further show that a non-bipartite quadrangulation of the projective plane can be transformed into an odd wheel by t-contractions and deletions of degree-2 vertices. WearXiv:1606.07662v3 fatcat:z2onopk4xvhezloj2elbuflere