8 citations · 19 across the 9 of their papers we have counts for
9 papers
Generalized spikes with circuits and cocircuits of different cardinalities
Nick Brettell, Kevin Grace
We consider matroids with the property that every subset of the ground set of size is contained in a -element circuit and every subset of size is contained in a -el…
A combinatorial bound on the number of distinct eigenvalues of a graph
Sarah Allred, Craig Erickson, Kevin Grace +2
The smallest possible number of distinct eigenvalues of a graph , denoted by , has a combinatorial bound in terms of unique shortest paths in the graph. In particular, $q(…
Matroid stratifications of hypergraph varieties, their realization spaces, and discrete conditional independence models
Oliver Clarke, Kevin Grace, Fatemeh Mohammadi +1
We study varieties associated to hypergraphs from the point of view of projective geometry and matroid theory. We describe their decompositions into matroid varieties, which may be…
On Density-Critical Matroids
Rutger Campbell, Kevin Grace, James Oxley +1
For a matroid having rank-one flats, the density is unless , in which case . A matroid is density-critical if all of its proper min…
On the Highly Connected Dyadic, Near-Regular, and Sixth-Root-of-Unity Matroids
Ben Clark, Kevin Grace, James Oxley +1
Subject to announced results by Geelen, Gerards, and Whittle, we completely characterize the highly connected members of the classes of dyadic, near-regular, and sixth-root-of-unit…
The Templates for Some Classes of Quaternary Matroids
Kevin Grace
Subject to hypotheses based on the matroid structure theory of Geelen, Gerards, and Whittle, we completely characterize the highly connected members of the class of golden-mean mat…
On perturbations of highly connected dyadic matroids
Kevin Grace, Stefan H. M. van Zwam
Geelen, Gerards, and Whittle [3] announced the following result: let be a prime power, and let be a proper minor-closed class of -representa…
The highly connected even-cycle and even-cut matroids
Kevin Grace, Stefan H. M. van Zwam
The classes of even-cycle matroids, even-cycle matroids with a blocking pair, and even-cut matroids each have hundreds of excluded minors. We show that the number of excluded minor…
Templates for Binary Matroids
Kevin Grace, Stefan H. M. van Zwam
A binary frame template is a device for creating binary matroids from graphic or cographic matroids. Such matroids are said to conform or coconform to the template. We introduce a…