Graphs without a rainbow path of length 3
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914637519257600 |
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| author | Babiński, Sebastian Grzesik, Andrzej |
| author_facet | Babiński, Sebastian Grzesik, Andrzej |
| contents | In 1959 Erdős and Gallai proved the asymptotically optimal bound for the maximum number of edges in graphs not containing a path of a fixed length. Here we study a rainbow version of their theorem, in which one considers $k \geq 1$ graphs on a common set of vertices not creating a path having edges from different graphs and asks for the maximum number of edges in each graph. We prove the asymptotically optimal bound in the case of a path on three edges and any $k \geq 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_02308 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Graphs without a rainbow path of length 3 Babiński, Sebastian Grzesik, Andrzej Combinatorics In 1959 Erdős and Gallai proved the asymptotically optimal bound for the maximum number of edges in graphs not containing a path of a fixed length. Here we study a rainbow version of their theorem, in which one considers $k \geq 1$ graphs on a common set of vertices not creating a path having edges from different graphs and asks for the maximum number of edges in each graph. We prove the asymptotically optimal bound in the case of a path on three edges and any $k \geq 1$. |
| title | Graphs without a rainbow path of length 3 |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2211.02308 |