Irreducibility of the Tutte polynomial of an embedded graph

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

Topological graph theory through matroid theory

A standard statement in undergraduate graph theory is that 'deletion and contraction are dual operations'. But this statement is only partially true, and completing it will take us on a route through graphs in surfaces to the world of delta-matroids. Along the way we'll see some of this general setting's advantages and challenges

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum