  A \textit{$t$-unit-bar representation} of a graph $G$ is an assignment of
sets of at most $t$ horizontal unit-length segments in the plane to the
vertices of $G$ so that (1) all of the segments are pairwise nonintersecting,
and (2) two vertices $x$ and $y$ are adjacent if and only if there is a
vertical channel of positive width connecting a segment assigned to $x$ and a
segment assigned to $y$ that intersects no other segment. The \textit{unit bar
visibility number} of a graph $G$, denoted $ub(G)$, is the minimum $t$ such
that $G$ has a $t$-unit-bar visibility representation. Our results include a
linear time algorithm that determines $ub(T)$ when $T$ is a tree, bounds on
$ub(K_{m,n})$ that determine $ub(K_{m,n})$ asymptotically when $n$ and $m$ are
asymptotically equal, and bounds on $ub(K_n)$ that determine $ub(K_n)$ exactly
when $n\equiv 1,2\pmod 6$.
