Showing 2024 · math.COShow all
3 papers · 2 filters
math.CO2024
On decomposition thresholds for odd-length cycles and other tripartite graphs
Darryn Bryant, Peter Dukes, Daniel Horsley +2
An (edge) decomposition of a graph is a set of subgraphs of whose edge sets partition the edge set of . Here we show, for each odd , that any graph of s…
math.CO2024
The balancing index over the alternating group
Peter Dukes, Georgia Penner
The balancing index of a polynomial is the least positive sum of coefficients in an integer linear combination of permuted copies of which pro…
math.CO2024
Duplicated Steiner triple systems with self-orthogonal near resolutions
Peter J. Dukes, Esther R. Lamken
A Steiner triple system, STS, is a family of -subsets (blocks) of a set of elements such that any two elements occur together in precisely one block. A collection of tr…