Permutation-partition pairs. II. Bounds on the genus of the amalgamation of graphs
Abstract: Bounds are derived on the extent to which the parameter can fail to be additive over disjoint permutations. This is done by associating an Eulerian digraph to each such pair and relating the maximum orbiticity to the decompositions of this digraph's arc set into arc disjoint cycles. These bounds are then applied to obtain information about the genus of the amalgamation of graphs.
- [S] Saul Stahl, Permutation-partition pairs: a combinatorial generalization of graph embeddings, Trans. Amer. Math. Soc. 259 (1980), no. 1, 129–145. MR 561828, https://doi.org/10.1090/S0002-9947-1980-0561828-2
- [W] David W. Walkup, How many ways can a permutation be factored into two 𝑛-cycles?, Discrete Math. 28 (1979), no. 3, 315–319. MR 548630, https://doi.org/10.1016/0012-365X(79)90138-9
- S. Stahl, Permutation-partition pairs: A combinatorial generalization of graph embeddings, Trans. Amer. Math. Soc. 259 (1980), 129-145. MR 561828 (82e:05065a)
- D. W. Walkup, How many ways can a permutation be factored into two -cycles?, Discrete Math. 28 (1979), 315-319. MR 548630 (81d:05005)
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