Gallai-Ramsey Numbers for $\ell$-Connected Graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909995758518272 |
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| author | Wang, Zhao Zhang, Lanyanni Wei, Meiqin Budden, Mark |
| author_facet | Wang, Zhao Zhang, Lanyanni Wei, Meiqin Budden, Mark |
| contents | Given a nonempty graph $G$, a collection of nonempty graphs $\cal{H}$, and a positive integer $k$, the Gallai-Ramsey number $\mathrm{gr}_k(G:\mathcal{H})$ is defined to be the minimum positive integer $n$ such that every exact $k$-edge-coloring of a complete graph $K_n$ contains either a rainbow copy of $G$ or a monochromatic copy of some element in $\mathcal{H}$. In this paper, we obtain some exact values and general lower and upper bounds for $\mathrm{gr}_k(G:\mathcal{F}^\ell)$, where $\mathcal{F}^\ell$ is the set of $\ell$-connected graphs and $G\in\{P_5, K_{1,3}\}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_13944 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gallai-Ramsey Numbers for $\ell$-Connected Graphs Wang, Zhao Zhang, Lanyanni Wei, Meiqin Budden, Mark Combinatorics 05C40, 05C55, 05D10 Given a nonempty graph $G$, a collection of nonempty graphs $\cal{H}$, and a positive integer $k$, the Gallai-Ramsey number $\mathrm{gr}_k(G:\mathcal{H})$ is defined to be the minimum positive integer $n$ such that every exact $k$-edge-coloring of a complete graph $K_n$ contains either a rainbow copy of $G$ or a monochromatic copy of some element in $\mathcal{H}$. In this paper, we obtain some exact values and general lower and upper bounds for $\mathrm{gr}_k(G:\mathcal{F}^\ell)$, where $\mathcal{F}^\ell$ is the set of $\ell$-connected graphs and $G\in\{P_5, K_{1,3}\}$. |
| title | Gallai-Ramsey Numbers for $\ell$-Connected Graphs |
| topic | Combinatorics 05C40, 05C55, 05D10 |
| url | https://arxiv.org/abs/2601.13944 |