Spanning Even Linear Forests with Isolated Edges Share the Anti-Ramsey Numbers of Perfect Matchings

Source abstract

The anti-Ramsey number $AR(n,F)$ is the maximum number of colors in an edge-coloring of the complete graph $K_n$ containing no rainbow copy of $F$. I prove that every spanning linear forest on an even number $n\ge6$ of vertices whose components have even orders and which has an isolated edge has the same anti-Ramsey number as a perfect matching on $n$ vertices. The orders of the longer path components may be different.