1 citations · 2 across the 7 of their papers we have counts for
7 papers
Planar Turán number of the 7-cycle
Ruilin Shi, Zach Walsh, Xingxing Yu
The of a graph is the maximum number of edges in an -vertex planar graph without as a subgraph. Let $C_{\e…
Matroid lifts and representability
Daniel Irving Bernstein, Zach Walsh
A 1965 result of Crapo shows that every elementary lift of a matroid can be constructed from a linear class of circuits of . In a recent paper, Walsh generalized this constr…
On the column number and forbidden submatrices for -modular matrices
Joseph Paat, Ingo Stallknecht, Zach Walsh +1
An integer matrix is -modular if the determinant of each submatrix of has absolute value at mo…
Small cocircuits in minimally vertically -connected matroids
James Oxley, Zach Walsh
Halin proved that every minimally -connected graph has a vertex of degree . More generally, does every minimally vertically -connected matroid have a -element cocircuit…
A new matroid lift construction and an application to group-labeled graphs
Zach Walsh
A well-known result of Brylawski constructs an elementary lift of a matroid from a linear class of circuits of . We generalize this result by showing how to construct a rank…
Excluding a line from -representable matroids
Jim Geelen, Peter Nelson, Zach Walsh
For each positive integer and each sufficiently large integer , we show that the maximum number of elements of a simple, rank-, -representable matroid with no…
The extremal function for geometry minors of matroids over prime fields
Peter Nelson, Zach Walsh
A frame template over a field describes the precise way in which a given -representable matroid is close to being a frame matroid. Our main result determines…