A note on tight cuts in matching-covered graphs

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