  A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the
alphabet $V$ such that letters $x$ and $y$, $x\neq y$, alternate in $w$ if and
only if $(x,y)\in E$. Halld\'{o}rsson et al.\ have shown that a graph is
word-representable if and only if it admits a so-called semi-transitive
orientation. A corollary to this result is that any 3-colorable graph is
word-representable.
  Akrobotu et al.\ have shown that a triangulation of a grid graph is
word-representable if and only if it is 3-colorable. This result does not hold
for triangulations of grid-covered cylinder graphs, namely, there are such
word-representable graphs with chromatic number 4. In this paper we show that
word-representability of triangulations of grid-covered cylinder graphs with
three sectors (resp., more than three sectors) is characterized by avoiding a
certain set of six minimal induced subgraphs (resp., wheel graphs $W_5$ and
$W_7$).
