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arXiv · 1908.04129

On the anti-Ramsey number of forests

Chunqiu Fang·Ervin Győri·Mei Lu·Jimeng Xiao
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Abstract

We call a subgraph of an edge-colored graph rainbow subgraph, if all of its edges have different colors. The anti-Ramsey number of a graph $G$ in a complete graph $K_{n}$, denoted by $ar(K_{n}, G)$, is the maximum number of colors in an edge-coloring of $K_{n}$ with no rainbow subgraph copy of $G$. In this paper, we determine the exact value of the anti-Ramsey number for star forests and the approximate value of the anti-Ramsey number for linear forests. Furthermore, we compute the exact value of $ar(K_{n}, 2P_{4})$ for $n\ge 8$ and $ar(K_{n}, S_{p,q})$ for large $n$, where $S_{p,q}$ is the double star with $p+q$ leaves.

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Chunqiu Fang, Ervin Győri, Mei Lu, Jimeng Xiao. 2019-08-12. On the anti-Ramsey number of forests. https://arxiv.org/abs/1908.04129

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