Transformations in closed 2-cell embeddings on surfaces preserving specified properties

Abstract

Consider a class script C sign of closed 2-cell embeddings on a closed surface F2, allowed to have multiple edges, such that for an embedding G ∈ script C sign each embedding which has G as a minor is also an element of script C sign. In this paper, we shall show that for any closed surface F2, there exists a natural number Nscript C sign(F2) such that any two elements G, G′ ∈ script C sign with |E(G)| = |E(G′)|≥Nscript C sign(F2) are connected in script C sign by a sequence of the local transformations. © 1999 Elsevier Science B.V. All rights reserved.