  Each (equigenerated) squarefree monomial ideal in the polynomial ring
$S=\mathbb{K}[x_1, \ldots, x_n]$ represents a family of subsets of $[n]$,
called a (uniform) clutter. In this paper, we introduce a class of uniform
clutters, called decomposable clutters, whose associated ideal has linear
quotients and hence linear resolution over all fields. We show that chordality
of these clutters guarantees the correctness of a conjecture raised by R. S.
Simon on extendable shellability of $d$-skeletons of a simplex $\langle [n]
\rangle$, for all $d$. We then prove this conjecture for $d \geq n-3$.
