The anti-Ramsey numbers of cliques in complete multi-partite graphs
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910286515011584 |
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| author | An, Yuyu Gyori, Ervin Li, Binlong |
| author_facet | An, Yuyu Gyori, Ervin Li, Binlong |
| contents | A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. Let $G$ and $H$ be two graphs. The anti-Ramsey number $\ar(G, H)$ is the maximum number of colors of an edge-coloring of $G$ that does not contain a rainbow copy of $H$. In this paper, we study the anti-Ramsey numbers of $K_k$ in complete multi-partite graphs. We determine the values of the anti-Ramsey numbers of $K_k$ in complete $k$-partite graphs and in balanced complete $r$-partite graphs for $r\geq k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01766 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The anti-Ramsey numbers of cliques in complete multi-partite graphs An, Yuyu Gyori, Ervin Li, Binlong Combinatorics 05D10 G.2.2 A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. Let $G$ and $H$ be two graphs. The anti-Ramsey number $\ar(G, H)$ is the maximum number of colors of an edge-coloring of $G$ that does not contain a rainbow copy of $H$. In this paper, we study the anti-Ramsey numbers of $K_k$ in complete multi-partite graphs. We determine the values of the anti-Ramsey numbers of $K_k$ in complete $k$-partite graphs and in balanced complete $r$-partite graphs for $r\geq k$. |
| title | The anti-Ramsey numbers of cliques in complete multi-partite graphs |
| topic | Combinatorics 05D10 G.2.2 |
| url | https://arxiv.org/abs/2401.01766 |