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The Tree of Cuts and Minimal k-Connected Graphs. / Karpov, D. V.

в: Journal of Mathematical Sciences (United States), Том 212, № 6, 2016, стр. 654-665.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Karpov, DV 2016, 'The Tree of Cuts and Minimal k-Connected Graphs', Journal of Mathematical Sciences (United States), Том. 212, № 6, стр. 654-665. https://doi.org/10.1007/s10958-016-2696-2

APA

Karpov, D. V. (2016). The Tree of Cuts and Minimal k-Connected Graphs. Journal of Mathematical Sciences (United States), 212(6), 654-665. https://doi.org/10.1007/s10958-016-2696-2

Vancouver

Karpov DV. The Tree of Cuts and Minimal k-Connected Graphs. Journal of Mathematical Sciences (United States). 2016;212(6):654-665. https://doi.org/10.1007/s10958-016-2696-2

Author

Karpov, D. V. / The Tree of Cuts and Minimal k-Connected Graphs. в: Journal of Mathematical Sciences (United States). 2016 ; Том 212, № 6. стр. 654-665.

BibTeX

@article{8003de66737146a6bf4c875960b017e4,
title = "The Tree of Cuts and Minimal k-Connected Graphs",
abstract = "A cut of a k-connected graph G is a k-element cutset of it, which contains at least one edge. The tree of cuts of a set[MediaObject not available: see fulltext.], consisting of pairwise independent cuts of a k-connected graph, is defined in the following way. Its vertices are the cuts of the set[MediaObject not available: see fulltext.]and the parts of the decomposition of G induced by these cuts. A part A is adjacent to a cut S if and only if A contains all the vertices of S and exactly one end of each edge of S. It is proved that the defined graph is a tree, some properties of which are similar to the corresponding properties of the classic tree of blocks and cutpoints. In the second part of the paper, the tree of cuts is used to study minimal k-connected graphs for k ≤ 5. Bibliography: 11 titles.",
keywords = "Bipartite Graph, Common Edge, Distinct Edge, Mutual Disposition, Minimal Part",
author = "Karpov, {D. V.}",
note = "Karpov, D.V. The Tree of Cuts and Minimal k-Connected Graphs. J Math Sci 212, 654–665 (2016). https://doi.org/10.1007/s10958-016-2696-2",
year = "2016",
doi = "10.1007/s10958-016-2696-2",
language = "English",
volume = "212",
pages = "654--665",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "6",

}

RIS

TY - JOUR

T1 - The Tree of Cuts and Minimal k-Connected Graphs

AU - Karpov, D. V.

N1 - Karpov, D.V. The Tree of Cuts and Minimal k-Connected Graphs. J Math Sci 212, 654–665 (2016). https://doi.org/10.1007/s10958-016-2696-2

PY - 2016

Y1 - 2016

N2 - A cut of a k-connected graph G is a k-element cutset of it, which contains at least one edge. The tree of cuts of a set[MediaObject not available: see fulltext.], consisting of pairwise independent cuts of a k-connected graph, is defined in the following way. Its vertices are the cuts of the set[MediaObject not available: see fulltext.]and the parts of the decomposition of G induced by these cuts. A part A is adjacent to a cut S if and only if A contains all the vertices of S and exactly one end of each edge of S. It is proved that the defined graph is a tree, some properties of which are similar to the corresponding properties of the classic tree of blocks and cutpoints. In the second part of the paper, the tree of cuts is used to study minimal k-connected graphs for k ≤ 5. Bibliography: 11 titles.

AB - A cut of a k-connected graph G is a k-element cutset of it, which contains at least one edge. The tree of cuts of a set[MediaObject not available: see fulltext.], consisting of pairwise independent cuts of a k-connected graph, is defined in the following way. Its vertices are the cuts of the set[MediaObject not available: see fulltext.]and the parts of the decomposition of G induced by these cuts. A part A is adjacent to a cut S if and only if A contains all the vertices of S and exactly one end of each edge of S. It is proved that the defined graph is a tree, some properties of which are similar to the corresponding properties of the classic tree of blocks and cutpoints. In the second part of the paper, the tree of cuts is used to study minimal k-connected graphs for k ≤ 5. Bibliography: 11 titles.

KW - Bipartite Graph

KW - Common Edge

KW - Distinct Edge

KW - Mutual Disposition

KW - Minimal Part

UR - http://www.scopus.com/inward/record.url?scp=84953390108&partnerID=8YFLogxK

U2 - 10.1007/s10958-016-2696-2

DO - 10.1007/s10958-016-2696-2

M3 - Article

AN - SCOPUS:84953390108

VL - 212

SP - 654

EP - 665

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 6

ER -

ID: 36925287