Maps and \(\Delta\)-matroids (Q2639862)

\(\Delta\)-matroids, recently introduced by the author, are combinatorial structures generalizing matroids. This paper associates a \(\Delta\)- matroid D(\({\mathcal M})\) to any pair \({\mathcal M}\neq (G,S)\) where G is a graph which is 2-cell imbedded in a compact surface S. If S is the sphere, D(\({\mathcal M})\) is the cycle matroid of G.