3 papers
math.CO2026
Skew circuits and circumference in a binary matroid
Sean McGuinness
Let C_1 and C_2 be skew circuits in a binary matroid having circumference c. For any positive integer k there is a constant a_k such that if min { |A| ; C_1 \subset A \subset E-A}…
math.CO2026
Short Rainbow Circuits in Regular Matroids
Sean McGuinness
DeVos et al conjectured that if is a simple, regular matroid and is a colouring of the elements of with colours, where each colour class has at least two eleme…
math.CO2024
Cyclic Orderings of Paving Matroids
Sean McGuinness
A matroid M is cyclically orderable if there is a cyclic permutation of the elements of M such that any r consecutive elements form a basis in M. An old conjecture of Kajitani, Miy…