Dillon Mayhew

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3 papers · 1 filter

math.CO2026

The excluded minors for $Z_{3}$ -gainable and regular biased graphs

Nick Brettell, Rutger Campbell, Daryl Funk +1

We prove that a biased graph is gainable over the group $Z_{3}$ if and only if it contains no minor isomorphic to $(4 K_{2}, \emptyset)$ , $\pm K_{3}$ , or $- K_{4}$ . We develo…

math.CO2026

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…

math.CO2024

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 $G$ . The nodes of the reduced clique graph are the maximal cliques of $G$ , and two nodes are joined…

The excluded minors for Z3​-gainable and regular biased graphs

Myhill-Nerode for hypergraphs and an application to gain-graphic matroids

Reduced clique graphs: a correction to "Chordal graphs and their clique graphs"

The excluded minors for $Z_{3}$ -gainable and regular biased graphs