Some results concerning the ends of minimal cuts of simple graphs

Xiaofeng Jia

Discussiones Mathematicae Graph Theory (2000)

  • Volume: 20, Issue: 1, page 139-142
  • ISSN: 2083-5892

Abstract

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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)|.

How to cite

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Xiaofeng Jia. "Some results concerning the ends of minimal cuts of simple graphs." Discussiones Mathematicae Graph Theory 20.1 (2000): 139-142. <http://eudml.org/doc/270224>.

@article{XiaofengJia2000,
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)|.},
author = {Xiaofeng Jia},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {cut; fragment; end; interference; vertex cut},
language = {eng},
number = {1},
pages = {139-142},
title = {Some results concerning the ends of minimal cuts of simple graphs},
url = {http://eudml.org/doc/270224},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Xiaofeng Jia
TI - Some results concerning the ends of minimal cuts of simple graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2000
VL - 20
IS - 1
SP - 139
EP - 142
AB - 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)|.
LA - eng
KW - cut; fragment; end; interference; vertex cut
UR - http://eudml.org/doc/270224
ER -

References

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  1. [1] B. Bollobas, Extremal Graph Theory (Academic Press, New York, 1978). Zbl0419.05031
  2. [2] H. Veldman, Non k-Critical Vertices in Graphs, Discrete Math. 44 (1983) 105-110, doi: 10.1016/0012-365X(83)90009-2. Zbl0542.05043

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