If D is a finite digraph, a directed cut is a subset of arcs in D having tail in some subset X ⊆ V(D) and head in V(D) X. In this paper we prove two general results concerning intersections between maximal paths, cycles and maximal directed cuts in D. As a direct consequence of these results, we deduce that there is a path, or a cycle, in D that crosses each maximal directed cut.

Intersection properties of maximal directed cuts in digraphs

Giampiero Chiaselotti
;
Tommaso Gentile
2017

Abstract

If D is a finite digraph, a directed cut is a subset of arcs in D having tail in some subset X ⊆ V(D) and head in V(D) X. In this paper we prove two general results concerning intersections between maximal paths, cycles and maximal directed cuts in D. As a direct consequence of these results, we deduce that there is a path, or a cycle, in D that crosses each maximal directed cut.
Directed Graphs; Paths; Directed Cuts
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/143687
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