Irreducibility of the Tutte polynomial of an embedded graph

Iain Moffatt, Joanna Ellis-Monaghan, Andrew Goodall, 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
JournalAlgebraic Combinatorics
Issue number2
Publication statusPublished - 2022

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