7 citations · 13 across the 5 of their papers we have counts for
8 papers
The optimal bound on the 3-independence number obtainable from a polynomial-type method
Lord C. Kavi, Mike Newman
A -independent set in a connected graph is a set of vertices such that any two vertices in the set are at distance greater than in the graph. The -independence number of…
Defining bicircular matroids in monadic logic
Daryl Funk, Dillon Mayhew, Mike Newman
We conjecture that the class of frame matroids can be characterised by a sentence in the monadic second-order logic of matroids, and we prove that there is such a characterisation…
Tree automata and pigeonhole classes of matroids: II
Daryl Funk, Dillon Mayhew, Mike Newman
Let be a sentence in the counting monadic second-order logic of matroids and let be a finite field. Hliněný's Theorem says that we can test whether -re…
Tree automata and pigeonhole classes of matroids: I
Daryl Funk, Dillon Mayhew, Mike Newman
Hlineny's Theorem shows that any sentence in the monadic second-order logic of matroids can be tested in polynomial time, when the input is limited to a class of F-representable ma…
Fractal classes of matroids
Dillon Mayhew, Mike Newman, Geoff Whittle
A minor-closed class of matroids is (strongly) fractal if the number of n-element matroids in the class is dominated by the number of n-element excluded minors. We conjecture that…
Yes, the "missing axiom" of matroid theory is lost forever
Dillon Mayhew, Mike Newman, Geoff Whittle
We prove there is no sentence in the monadic second-order language MS0 that characterises when a matroid is representable over at least one field, and no sentence that characterise…
Is the missing axiom of matroid theory lost forever?
Dillon Mayhew, Mike Newman, Geoff Whittle
We conjecture that it is not possible to finitely axiomatize matroid representability in monadic second-order logic for matroids, and we describe some partial progress towards this…
A note on packing spanning trees in graphs and bases in matroids
Robert F. Bailey, Mike Newman, Brett Stevens
We consider the class of graphs for which the edge connectivity is equal to the maximum number of edge-disjoint spanning trees, and the natural generalization to matroids, where th…