Discussiones
Mathematicae Graph Theory 20(1) (2000) 139-142
DOI: https://doi.org/10.7151/dmgt.1113
SOME RESULTS CONCERNING THE ENDS OF MINIMAL CUTS OF SIMPLE GRAPHS
Xiaofeng Jia
Department of Mathematics
Taiyuan University of Technology (West Campus)
Taiyuan, Shanxi, P.R. China 030024
Abstract
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.
1991 Mathematics Subject Classification: 05C35, 05C40.
References
[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. |
Received 14 October 1999
Revised 24 February 2000
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