On f-Derangements and Decomposing Bipartite Graphs into Paths

Michael Plantholt, Hamidreza Habibi, Benjamin Mussell

Let $f:\{1,...,n\}\to \{1,...,n\}$ be a function (not necessarily one-to-one). An $f-derangement$ is a permutation $g:\{1,...,n\}\to \{1,...,n\}$ such that…