Ramsey goodness of complete multipartite graphs with one large part
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866916049369169920 |
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| author | Mi, Shaonan Wang, Ye |
| author_facet | Mi, Shaonan Wang, Ye |
| contents | For graph $G$, a connected graph $H$ of order $n$ is said to be $G$-good if $r(G,H)=(χ(G)-1)(n-1)+s(G)$, where $χ(G)$ is the chromatic number of $G$ and $s(G)$ is the minimum size of a color class in a $χ(G)$-coloring of $G$. Let $K_{p+1}(α;n)$ denote the complete $(p+1)$-partite graph with $p$ partite sets of size $α$ and one partite set of size $n$. We determine all graphs $G$ for which $K_{p+1}(α;n)$ is $G$-good for large $n$. The characterization depends on the parameter $\mathrm{snd}(α)$, the smallest non-divisor of $α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26826 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ramsey goodness of complete multipartite graphs with one large part Mi, Shaonan Wang, Ye Combinatorics For graph $G$, a connected graph $H$ of order $n$ is said to be $G$-good if $r(G,H)=(χ(G)-1)(n-1)+s(G)$, where $χ(G)$ is the chromatic number of $G$ and $s(G)$ is the minimum size of a color class in a $χ(G)$-coloring of $G$. Let $K_{p+1}(α;n)$ denote the complete $(p+1)$-partite graph with $p$ partite sets of size $α$ and one partite set of size $n$. We determine all graphs $G$ for which $K_{p+1}(α;n)$ is $G$-good for large $n$. The characterization depends on the parameter $\mathrm{snd}(α)$, the smallest non-divisor of $α$. |
| title | Ramsey goodness of complete multipartite graphs with one large part |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.26826 |