Multicolor Erdős--Rogers Functions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908539863171072 |
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| author | Liu, Hong Luo, Haoran Ouyang, Minghui |
| author_facet | Liu, Hong Luo, Haoran Ouyang, Minghui |
| contents | In this paper, we study a multicolor variant of Erdős--Rogers functions. Let $f_{α_s; K_{i_1}, \cdots, K_{i_t}}(n)$ be the largest integer $m$ such that there is always an induced $K_s$-free subgraph of size $m$ in every $n$-vertex graph with a $t$-edge-coloring in which the edges with the $j$-th color induce no copy of $K_{i_j}$. We establish both upper and lower bounds for this multicolor version. Specifically, we show that $f_{α_5; K_3, K_3}(n) = n^{1/2+o(1)}$, $Ω(n^{5/11}) \le f_{α_5; K_3, K_3, K_3}(n) \le n^{1/2+o(1)}$, and $Ω(n^{20/61}) \le f_{α_5; K_3, K_3, K_3, K_3}(n) \le n^{1/3+o(1)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_12044 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multicolor Erdős--Rogers Functions Liu, Hong Luo, Haoran Ouyang, Minghui Combinatorics 05C55 (primary), 05D10 (Secondary) In this paper, we study a multicolor variant of Erdős--Rogers functions. Let $f_{α_s; K_{i_1}, \cdots, K_{i_t}}(n)$ be the largest integer $m$ such that there is always an induced $K_s$-free subgraph of size $m$ in every $n$-vertex graph with a $t$-edge-coloring in which the edges with the $j$-th color induce no copy of $K_{i_j}$. We establish both upper and lower bounds for this multicolor version. Specifically, we show that $f_{α_5; K_3, K_3}(n) = n^{1/2+o(1)}$, $Ω(n^{5/11}) \le f_{α_5; K_3, K_3, K_3}(n) \le n^{1/2+o(1)}$, and $Ω(n^{20/61}) \le f_{α_5; K_3, K_3, K_3, K_3}(n) \le n^{1/3+o(1)}$. |
| title | Multicolor Erdős--Rogers Functions |
| topic | Combinatorics 05C55 (primary), 05D10 (Secondary) |
| url | https://arxiv.org/abs/2509.12044 |