An edge cut C of a graph G is tight if $|C\cap M|=1$ for every perfect matching M of G. Barrier cuts and 2-separation cuts are called ELP-cuts, which are two important types of tight cuts in matching covered graphs. Edmonds, Lovász and Pulleyblank proved that if a matching covered graph has a nontrivial tight cut, then it also has a nontrivial ELP-cut. Carvalho, Lucchesi, and Murty made a stronger conjecture: given any nontrivial tight cut C in a matching covered graph G, there exists a nontrivial ELP-cut D in G which does not cross C. We confirm the conjecture in this paper.

中文翻译：

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匹配覆盖图中的层流紧密切割

图G的边割C是紧的，如果$|C\cap 米|=1$每一个完美匹配，中号的摹。Barrier cut 和 2-separation cuts 被称为ELP-cuts，它们是匹配覆盖图的两种重要的紧割类型。Edmonds、Lovász 和 Pulleyblank 证明，如果匹配的覆盖图有一个非平凡的紧割，那么它也有一个非平凡的 ELP 割。卡瓦略，卢凯西和穆尔蒂制成更强的猜想：任何给定的非平凡紧切Ç在匹配覆盖图ģ，存在一个非平凡ELP切d在ģ其不跨Ç。我们证实了本文的猜想。