2 papers
math.CO2024
Balanced 1-Factorisations of 3- and 4-Regular Circulant Graphs
Jeremy Mitchell
We investigate 1-factorisations in which the 2-regular graphs that occur as the union of a pair of 1-factors appear an equal number of times across the unions of all pairs of 1-fac…
math.CO2023
An Infinite Family of Connected 1-Factorisations of Complete 3-Uniform Hypergraphs
Barbara Maenhaut, Jeremy Mitchell, Anna Puskas
A connected 1-factorisation is a 1-factorisation of a hypergraph for which the union of each pair of distinct 1-factors is a connected hypergraph. A uniform 1-factorisation is a 1-…