A linear upper bound for zero-sum Ramsey numbers of bounded degree graphs
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917469443063808 |
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| author | Katz, Jasmin Lian, Xiaopan Malekshahian, Alexandru Shapiro, Andrey |
| author_facet | Katz, Jasmin Lian, Xiaopan Malekshahian, Alexandru Shapiro, Andrey |
| contents | Let $G$ be a graph and $Γ$ a finite abelian group. The zero-sum Ramsey number of $G$ over $Γ$, denoted by $R(G, Γ)$, is the smallest positive integer $t$ (if it exists) such that any edge-colouring $c:E(K_t)\toΓ$ contains a copy of $G$ with $\sum_{e\in E(G)}c(e)=0_Γ$.
We prove a linear upper bound $R(G, Γ)\leq Cn$ that holds for every $n$-vertex graph $G$ with bounded maximum degree and every finite abelian group $Γ$ with $|Γ|$ dividing $e(G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A linear upper bound for zero-sum Ramsey numbers of bounded degree graphs Katz, Jasmin Lian, Xiaopan Malekshahian, Alexandru Shapiro, Andrey Combinatorics Let $G$ be a graph and $Γ$ a finite abelian group. The zero-sum Ramsey number of $G$ over $Γ$, denoted by $R(G, Γ)$, is the smallest positive integer $t$ (if it exists) such that any edge-colouring $c:E(K_t)\toΓ$ contains a copy of $G$ with $\sum_{e\in E(G)}c(e)=0_Γ$. We prove a linear upper bound $R(G, Γ)\leq Cn$ that holds for every $n$-vertex graph $G$ with bounded maximum degree and every finite abelian group $Γ$ with $|Γ|$ dividing $e(G)$. |
| title | A linear upper bound for zero-sum Ramsey numbers of bounded degree graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2512.17790 |