Edmonds, Lovász, and Pulleyblank showed that if a matching covered graph
has a nontrivial tight cut, then it also has a nontrivial ELP-cut. Carvalho et
al. gave a stronger conjecture: if a matching covered graph has a nontrivial
tight cut $C$, then it also has a nontrivial ELP-cut that does not cross $C$.
Chen, et al gave a proof of the conjecture. This note is inspired by the paper
of Carvalho et al. We give a simplified proof of the conjecture, and prove the
following result which is slightly stronger than the conjecture: if a
nontrivial tight cut $C$ of a matching covered graph $G$ is not an ELP-cut,
then there is a sequence $G_1=G, G_2,\ldots,G_r, r\geq2$ of matching covered
graphs, such that for $i=1, 2,\ldots, r-1$, $G_i$ has an ELP-cut $C_i$, and
$G_{i+1}$ is a $C_i$-contraction of $G_i$, and $C$ is a $2$-separation cut of
$G_r$.