On the Turán number of double stars
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915941974016000 |
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| author | Hu, Ping Lan, Ting |
| author_facet | Hu, Ping Lan, Ting |
| contents | The Turán number of a graph $F$, $ex(n,F)$, is the maximum number of edges in a graph on $n$ vertices which does not contain $F$ as a subgraph. Let $S_{a,b}$ denote a double star with a central edge $uv$, $a$ leaves connected to $u$ and $b$ leaves connected to $v$. The function $ex(n,S_{a,b})$ has been studied for $a=1,2$, their extremal graphs are disjoint copies of $K_{a+b+1}$ and either a small clique or a near $b$-regular graph. In this paper, we further study $ex(n,S_{3,b})$ and determine the extremal graphs, which have more structures than those of $a=1,2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15806 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Turán number of double stars Hu, Ping Lan, Ting Combinatorics The Turán number of a graph $F$, $ex(n,F)$, is the maximum number of edges in a graph on $n$ vertices which does not contain $F$ as a subgraph. Let $S_{a,b}$ denote a double star with a central edge $uv$, $a$ leaves connected to $u$ and $b$ leaves connected to $v$. The function $ex(n,S_{a,b})$ has been studied for $a=1,2$, their extremal graphs are disjoint copies of $K_{a+b+1}$ and either a small clique or a near $b$-regular graph. In this paper, we further study $ex(n,S_{3,b})$ and determine the extremal graphs, which have more structures than those of $a=1,2$. |
| title | On the Turán number of double stars |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.15806 |