On a rainbow version of Dirac's theorem
For a collection $\mathbf{G}=\{G_1,\dots, G_s\}$ of not necessarily distinct graphs on the same vertex set $V$, a graph $H$ with vertices in $V$ is a $\mathbf{G}$-transversal if there exists a bijection $\phi:E(H)\rightarrow [s]$ such that $e\in E(G_{\phi(e)})$ for all $e\in E(H)$. We prove that for...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
19 May 2020
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| In: |
Bulletin of the London Mathematical Society
Year: 2020, Volume: 52, Issue: 3, Pages: 498-504 |
| ISSN: | 1469-2120 |
| Online Access: |
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| Author Notes: | Felix Joos and Jaehoon Kim |
| Summary: | For a collection $\mathbf{G}=\{G_1,\dots, G_s\}$ of not necessarily distinct graphs on the same vertex set $V$, a graph $H$ with vertices in $V$ is a $\mathbf{G}$-transversal if there exists a bijection $\phi:E(H)\rightarrow [s]$ such that $e\in E(G_{\phi(e)})$ for all $e\in E(H)$. We prove that for $|V|=s\geq 3$ and $\delta(G_i)\geq s/2$ for each $i\in [s]$, there exists a $\mathbf{G}$-transversal that is a Hamilton cycle. This confirms a conjecture of Aharoni. We also prove an analogous result for perfect matchings. |
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| Item Description: | Gesehen am 27.07.2022 |
| Physical Description: | Online Resource |
| ISSN: | 1469-2120 |