The exact value of $c_1(K_{2,n})$
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918359492198400 |
|---|---|
| author | Mori, Hiroaki |
| author_facet | Mori, Hiroaki |
| contents | For a graph $G$, let $c_1(G)$ be the largest distortion necessary to embed any shortest-path metric on $G$ into $\ell_1$, and for any natural number $n,m\in\mathbb{N}$, denote $K_{n,m}$ as the complete bipartite graph. In this note, we caculate the value of $c_1(K_{2,n})$, more precisely we prove $c_1(K_{2,n})=\frac{3k-2}{2k-1}$ where $k=\lceil\frac{n}{2}\rceil$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23745 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The exact value of $c_1(K_{2,n})$ Mori, Hiroaki Combinatorics Discrete Mathematics For a graph $G$, let $c_1(G)$ be the largest distortion necessary to embed any shortest-path metric on $G$ into $\ell_1$, and for any natural number $n,m\in\mathbb{N}$, denote $K_{n,m}$ as the complete bipartite graph. In this note, we caculate the value of $c_1(K_{2,n})$, more precisely we prove $c_1(K_{2,n})=\frac{3k-2}{2k-1}$ where $k=\lceil\frac{n}{2}\rceil$. |
| title | The exact value of $c_1(K_{2,n})$ |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2602.23745 |