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Settling the Nonorientable Genus of the Nearly Complete Bipartite Graphs

Singh, Warren ; Sun, Timothy

Graphs and combinatorics, 2023-10, Vol.39 (5), Article 96 [Periódico revisado por pares]

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Título:
Settling the Nonorientable Genus of the Nearly Complete Bipartite Graphs
Autor: Singh, Warren ; Sun, Timothy
Assuntos: Combinatorics ; Diamonds ; Engineering Design ; Graph theory ; Graphs ; Mathematics ; Mathematics and Statistics ; Original Paper
É parte de: Graphs and combinatorics, 2023-10, Vol.39 (5), Article 96
Descrição: A graph is said to be nearly complete bipartite if it can be obtained by deleting a set of independent edges from a complete bipartite graph. The nonorientable genus of such graphs is known except in a few cases where the sizes of the partite classes differ by at most one, and a maximum matching is deleted. We resolve these missing cases using three classic tools for constructing genus embeddings of the complete bipartite graphs: current graphs, diamond sums, and the direct rotation systems of Ringel.
Editor: Tokyo: Springer Japan
Idioma: Inglês

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