Irreducibility of the Tutte polynomial of an embedded graph

Joanna Ellis-Monaghan, Andrew Goodall, Iain Moffatt, Steven Noble, Lluis Vena

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We prove that the ribbon graph polynomial of a graph embedded in an orientable surface is irreducible if and only if the embedded graph is neither the disjoint union nor the join of embedded graphs. This result is analogous to the fact that the Tutte polynomial of a graph is irreducible if and only if the graph is connected and non-separable.
Original languageEnglish
Pages (from-to)1337-1351
Number of pages15
JournalAlgebraic Combinatorics
Issue number6
Early online date19 Dec 2022
Publication statusE-pub ahead of print - 19 Dec 2022

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