Permutation-partition pairs: a combinatorial generalization of graph embeddings
Saul Stahl · Transactions of the American Mathematical Society · 1980
Permutation-partition pairs are a purely combinatorial generalization of graph embeddings. Some parameters are defined here for these pairs and several theorems are proved. These results are strong enough to prove virtually all the known theoretical informaton about the genus parameter as well as a new theorem regarding the genus of the amalgamation of two graphs over three points.