论文标题
有限公制树的等距嵌入到$（\ mathbb {r}^n，d_ {1}）$和$（\ mathbb {r}^n，d _ {\ infty}）$
Isometric Embeddings of Finite Metric Trees into $(\mathbb{R}^n,d_{1})$ and $(\mathbb{R}^n,d_{\infty})$
论文作者
论文摘要
我们将有限公制树的等距嵌入到$（\ Mathbb {r}^n，d_ {1}）$和$（\ Mathbb {r}^n，d _ {\ infty}）$中。我们证明，当有限的公制树可以嵌入$（\ mathbb {r}^n，d_ {1}）$时，仅当其叶子的数量最多为$ 2N $时。我们表明，最多有$ 2^n $叶子的有限星形树可以嵌入到$（\ Mathbb {r}^{n}，d _ {\ infty}）$和有限的公制树中，并具有$ 2^n $叶子超过$ 2^n $ sebs nosemetry嵌入$（ d _ {\ infty}）$。我们猜想，最多有$ 2^n $叶子的任意有限公制树可以将其嵌入$（\ mathbb {r}^{n}，d _ {\ infty}）$中。
We investigate isometric embeddings of finite metric trees into $(\mathbb{R}^n,d_{1})$ and $( \mathbb{R}^n, d_{\infty})$. We prove that a finite metric tree can be isometrically embedded into $(\mathbb{R}^n,d_{1})$ if and only if the number of its leaves is at most $2n$. We show that a finite star tree with at most $2^n$ leaves can be isometrically embedded into $(\mathbb{R}^{n}, d_{\infty})$ and a finite metric tree with more than $2^n$ leaves cannot be isometrically embedded into $(\mathbb{R}^{n}, d_{\infty})$. We conjecture that an arbitrary finite metric tree with at most $2^n$ leaves can be isometrically embedded into $(\mathbb{R}^{n}, d_{\infty})$.
