  A piecewise linear curve in the plane made up of $k+1$ line segments, each of
which is either horizontal or vertical, with consecutive segments being of
different orientation is called a $k$-bend path. Given a graph $G$, a
collection of $k$-bend paths in which each path corresponds to a vertex in $G$
and two paths have a common point if and only if the vertices corresponding to
them are adjacent in $G$ is called a $B_k$-VPG representation of $G$.
Similarly, a collection of $k$-bend paths each of which corresponds to a vertex
in $G$ is called an $B_k$-EPG representation of $G$ if any two paths have a
line segment of non-zero length in common if and only if their corresponding
vertices are adjacent in $G$. The VPG bend-number $b_v(G)$ of a graph $G$ is
the minimum $k$ such that $G$ has a $B_k$-VPG representation. Similarly, the
EPG bend-number $b_e(G)$ of a graph $G$ is the minimum $k$ such that $G$ has a
$B_k$-EPG representation. Halin graphs are the graphs formed by taking a tree
with no degree $2$ vertex and then connecting its leaves to form a cycle in
such a way that the graph has a planar embedding. We prove that if $G$ is a
Halin graph then $b_v(G) \leq 1$ and $b_e(G) \leq 2$. These bounds are tight.
In fact, we prove the stronger result that if $G$ is a planar graph formed by
connecting the leaves of any tree to form a simple cycle, then it has a
VPG-representation using only one type of 1-bend paths and an
EPG-representation using only one type of 2-bend paths.
