Permutation-partition pairs. II. Bounds on the genus of the amalgamation of graphs
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- by Saul Stahl PDF
- Trans. Amer. Math. Soc. 271 (1982), 175-182 Request permission
Abstract:
Bounds are derived on the extent to which the parameter $\mu (P, \prod )$ 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 $\mu (P, \prod )$ 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.References
- Saul Stahl, Permutation-partition pairs: a combinatorial generalization of graph embeddings, Trans. Amer. Math. Soc. 259 (1980), no. 1, 129–145. MR 561828, DOI 10.1090/S0002-9947-1980-0561828-2
- 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, DOI 10.1016/0012-365X(79)90138-9
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 271 (1982), 175-182
- MSC: Primary 05C10
- DOI: https://doi.org/10.1090/S0002-9947-1982-0648084-3
- MathSciNet review: 648084