45 citations · 494 across the 40 of their papers we have counts for
43 papers
Polynomial invariants of cyclically ordered graphs
Paul Bratch, M. N. Ellingham, Joanna A. Ellis-Monaghan +2
Cyclically ordered graphs, or cogs, sit between abstract graphs and cellularly embedded graphs. They arise naturally in topological graph theory, knot theory, and mathematical biol…
A coarse Tutte polynomial for hypermaps
Joanna A. Ellis-Monaghan, Iain Moffatt, Steven Noble
We give an analogue of the Tutte polynomial for hypermaps. This polynomial can be defined as either a sum over subhypermaps, or recursively through deletion-contraction reductions…
Tensor products of multimatroids and a Brylawski-type formula for the transition polynomial
Iain Moffatt, Steven Noble, Maya Thompson
Brylawski's tensor product formula expresses the Tutte polynomial of the tensor product of two graphs or matroids in terms of Tutte polynomials arising from the tensor factors. Ana…
The critical group of a combinatorial map
Criel Merino, Iain Moffatt, Steven Noble
Motivated by the appearance of embeddings in the theory of chip firing and the critical group of a graph, we introduce a version of the critical group (or sandpile group) for combi…
Types of embedded graphs and their Tutte polynomials
Stephen Huggett, Iain Moffatt
We take an elementary and systematic approach to the problem of extending the Tutte polynomial to the setting of embedded graphs. Four notions of embedded graphs arise naturally wh…
Irreducibility of the Tutte polynomial of an embedded graph
Joanna A. Ellis-Monaghan, Andrew J. Goodall, Iain Moffatt +2
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 o…