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arXiv · 2610.11441

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

Ali Ghalavand
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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.

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Ali Ghalavand. 2026-10-08. Spanning Even Linear Forests with Isolated Edges Share the Anti-Ramsey Numbers of Perfect Matchings. https://arxiv.org/abs/2610.11441

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