Permutation-Partition Pairs: A Combinatorial Generalization of Graph Embeddings

Saul Stahl

Type: Article

Publication Date: 1980-05-01

Citations: 11

DOI: https://doi.org/10.2307/1998149

Abstract

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.

Locations

Transactions of the American Mathematical Society - View - PDF

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Works That Cite This (9)

Action	Title	Year	Authors
+	A note on groups and permutation-partition pairs	1989	Attilia Cerè Anna Donati Massimo Ferri
+	The orientable genus is nonadditive	1986	Dan Archdeacon
+	An Euler‐genus approach to the calculation of the crosscap‐number polynomial	2017	Yichao Chen Jonathan L. Gross
+ PDF Chat	Permutation-partition pairs. II. Bounds on the genus of the amalgamation of graphs	1982	Saul Stahl
+	The genus of the 2‐amalgamations of graphs	1981	Richard W. Decker Henry Glover John Philip Huneke
+	The nonorientable genus is additive	1986	Dan Archdeacon
+	On the average genus of the random graph	1995	Saul Stahl
+	The Genus of Amalgamations	1989	Dan Archdeacon
+ PDF Chat	Erratum to: “Permutation-partition pairs: a combinatorial generalization of graph embeddings”	1981	Saul Stahl

Works Cited by This (5)

Action	Title	Year	Authors
+	Ramified coverings of Riemann surfaces	1962	Dale Husemöller
+ PDF Chat	Additivity of the genus of a graph	1962	Joseph Battle Frank Harary Yukihiro Kodama
+	An additivity theorem for maximum genus of a graph	1978	Charles H. C. Little Richard D. Ringeisen
+	A Kuratowski-type theorem for the maximum genus of a graph	1972	E. A. Nordhaus Richard D. Ringeisen B. M. Stewart Arthur T. White
+ PDF Chat	On the genus of an n-connected graph	1964	F. Harary Yuya Kodama