Laminar tight cuts in matching covered graphs
نویسندگان
چکیده
An edge cut C of a graph G is tight if |C∩M|=1 for every perfect matching M G. Barrier cuts and 2-separation are called ELP-cuts, which two important types in covered graphs. Edmonds, Lovász Pulleyblank proved that has nontrivial cut, then it also ELP-cut. Carvalho, Lucchesi, Murty made stronger conjecture: given any G, there exists ELP-cut D does not cross C. We confirm the conjecture this paper.
منابع مشابه
On Perfect Matchings in Matching Covered Graphs
Let G be a matching-covered graph, i.e., every edge is contained in a perfect matching. An edge subsetX ofG is feasible if there exists two perfect matchingsM1 andM2 such that |M1∩X| 6≡ |M2∩X| (mod 2). Lukot’ka and Rollová proved that an edge subset X of a regular bipartite graph is not feasible if and only if X is switching-equivalent to ∅, and they further ask whether a non-feasible set of a ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2021
ISSN: ['0095-8956', '1096-0902']
DOI: https://doi.org/10.1016/j.jctb.2021.05.003