Geodesic
Some results concerning the ends of minimal cuts of simple graphs
Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 1, pp. 139-142.

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Let S be a cut of a simple connected graph G. If S has no proper subset that is a cut, we say S is a minimal cut of G. To a minimal cut S, a connected component of G-S is called a fragment. And a fragment with no proper subset that is a fragment is called an end. In the paper ends are characterized and it is proved that to a connected graph G = (V,E), the number of its ends Σ ≤ |V(G)|.
Keywords: cut, fragment, end, interference 
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Jia, Xiaofeng. Some results concerning the ends of minimal cuts of simple graphs. Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 1, pp. 139-142. http://geodesic.mathdoc.fr/item/DMGT_2000_20_1_a10/

[1] B. Bollobas, Extremal Graph Theory (Academic Press, New York, 1978).

[2] H. Veldman, Non k-Critical Vertices in Graphs, Discrete Math. 44 (1983) 105-110, doi: 10.1016/0012-365X(83)90009-2.