3 problems

Let $K_{n,n}$ be the complete bipartite graph with $n$ vertices in each part. A 1-factorisation is a partition of the edges into 1-factors; the cycles of a 1-factorisation are the…

Let $K_{n,n}$ be the complete bipartite graph with $n$ vertices in each part. A 1-factorisation is a partition of the edges into 1-factors, and it is perfect when the union of ever…

The multipartite semiregular factorisation conjecture. If $n\to\infty$ with $2\le m\le n$ and $1\le k=o(m)$, then