Sabotage the Mantel Theorem
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866915365480562688 |
|---|---|
| author | Behague, Natalie Chakraborti, Debsoumya Liu, Xizhi |
| author_facet | Behague, Natalie Chakraborti, Debsoumya Liu, Xizhi |
| contents | One of the earliest results in extremal graph theory, Mantel's theorem, states that the maximum number of edges in a triangle-free graph $G$ on $n$ vertices is $\lfloor n^2/4 \rfloor$. We investigate how this extremal bound is affected when $G$ is additionally required to contain a prescribed graph $\mathbb{P}$ as a subgraph. We establish general upper and lower bounds for this problem, which are tight in the exponent for random triangle-free graphs and graphs generated by the triangle-free process, when the size of $\mathbb{P}$ lies within certain ranges. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23794 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sabotage the Mantel Theorem Behague, Natalie Chakraborti, Debsoumya Liu, Xizhi Combinatorics One of the earliest results in extremal graph theory, Mantel's theorem, states that the maximum number of edges in a triangle-free graph $G$ on $n$ vertices is $\lfloor n^2/4 \rfloor$. We investigate how this extremal bound is affected when $G$ is additionally required to contain a prescribed graph $\mathbb{P}$ as a subgraph. We establish general upper and lower bounds for this problem, which are tight in the exponent for random triangle-free graphs and graphs generated by the triangle-free process, when the size of $\mathbb{P}$ lies within certain ranges. |
| title | Sabotage the Mantel Theorem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2506.23794 |