Geodesic
The structure of directed forests of minimal weight: algebra of subsets of the set of vertices
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XI, Tome 488 (2019), pp. 5-30

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An embedded system of algebras of subsets of the set of vertices of weighted digraph is constructed, and the properties of spanning minimal forests are studied by restricting them to atoms of the corresponding algebras. 
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     author = {V. A. Buslov},
     title = {The structure of directed forests of minimal weight: algebra of subsets of the set of vertices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--30},
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     volume = {488},
     year = {2019},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_488_a0/}
}
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V. A. Buslov. The structure of directed forests of minimal weight: algebra of subsets of the set of vertices. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XI, Tome 488 (2019), pp. 5-30. http://geodesic.mathdoc.fr/item/ZNSL_2019_488_a0/