10 citations · 40 across the 33 of their papers we have counts for
39 papers
The excluded minors for -gainable and regular biased graphs
Nick Brettell, Rutger Campbell, Daryl Funk +1
We prove that a biased graph is gainable over the group if and only if it contains no minor isomorphic to , , or . We develo…
Myhill-Nerode for hypergraphs and an application to gain-graphic matroids
Daryl Funk, Angus Matthews, Dillon Mayhew
We present a Myhill-Nerode theorem for hypergraphs. The theorem involves an operation which takes two input structures and produces a hypergraph as output. Using this operation, we…
Dominic Welsh: his work and influence
Graham Farr, Dillon Mayhew, James Oxley
We review the work of Dominic Welsh (1938-2023), tracing his remarkable influence through his theorems, expository writing, students, and interactions. He was particularly adept at…
Monadic transductions and definable classes of matroids
Susan Jowett, Dillon Mayhew, Songbao Mo +1
A transduction provides us with a way of using the monadic second-order language of a structure to make statements about a derived structure. Any transduction induces a relation on…
Supersolvable saturated matroids and chordal graphs
Dillon Mayhew, Andrew Probert
A matroid is supersolvable if it has a maximal chain of flats each of which is modular. A matroid is saturated if every round flat is modular. In this article we present supersolva…
Reduced clique graphs: a correction to "Chordal graphs and their clique graphs"
Dillon Mayhew, Andrew Probert
Galinier, Habib, and Paul introduced the reduced clique graph of a chordal graph . The nodes of the reduced clique graph are the maximal cliques of , and two nodes are joined…