  A hypertree is a connected hypergraph without cycles. Further a hypertree is
called an $r$-tree if, additionally, it is $r$-uniform. Note that 2-trees are
just ordinary trees. A classical result states that for any 2-tree $T$ with
characteristic polynomial $\phi_T(\lambda)$ and matching polynomial
$\varphi_T(\lambda)$, then $\phi_T(\lambda)=\varphi_T(\lambda).$ More
generally, suppose $\mathcal{T}$ is an $r$-tree of size $m$ with $r\geq2$. In
this paper, we extend the above classical relationship to $r$-trees and
establish that \[ \phi_{\mathcal{T}}(\lambda)=\prod_{H \sqsubseteq
\mathcal{T}}\varphi_{H}(\lambda)^{a_{H}}, \] where the product is over all
connected subgraphs $H$ of $\mathcal{T}$, and the exponent $a_{H}$ of the
factor $\varphi_{H}(\lambda)$ can be written as \[
a_H=b^{m-e(H)-|\partial(H)|}c^{e(H)}(b-c)^{|\partial(H)|},
  \] where $e(H)$ is the size of $H$, $\partial(H)$ is the boundary of $H$, and
$b=(r-1)^{r-1}, c=r^{r-2}$. In particular, for $r=2$, the above correspondence
reduces to the classical result for ordinary trees. In addition, we resolve a
conjecture by Clark-Cooper [{\em Electron. J. Combin.}, 2018] and show that for
any subgraph $H$ of an $r$-tree $\mathcal{T}$ with $r\geq3$,
$\varphi_H(\lambda)$ divides $\phi_{\mathcal{T}}(\lambda)$, and additionally
$\phi_H(\lambda)$ divides $\phi_{\mathcal{T}}(\lambda)$, if either $r\geq 4$ or
$H$ is connected when $r=3$. Moreover, a counterexample is given for the case
when $H$ is a disconnected subgraph of a 3-tree.
