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Title: On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components

Abstract

A graph is called cyclically 4-edge-connected if removing any three edges from it results in a graph in which at most one connected component contains a cycle. A 3-connected graph is 4-edge-connected if and only if removing any three edges from it results in either a connected graph or a graph with exactly two connected components one of which is a single-vertex one. We show how to associate with any 3-connected graph a tree of components such that every component is a 3-connected and cyclically 4-edge-connected graph.

Authors:
 [1]
  1. St.Petersburg Department of Steklov Institute of Mathematics and Peter the Great St.Petersburg Polytechnic University (Russian Federation)
Publication Date:
OSTI Identifier:
22774015
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 232; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; DECOMPOSITION; GRAPH THEORY; MATHEMATICAL SOLUTIONS

Citation Formats

Pastor, A. V., E-mail: pastor@pdmi.ras.ru. On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3859-0.
Pastor, A. V., E-mail: pastor@pdmi.ras.ru. On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components. United States. doi:10.1007/S10958-018-3859-0.
Pastor, A. V., E-mail: pastor@pdmi.ras.ru. Sun . "On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components". United States. doi:10.1007/S10958-018-3859-0.
@article{osti_22774015,
title = {On the Decomposition of a 3-Connected Graph into Cyclically 4-Edge-Connected Components},
author = {Pastor, A. V., E-mail: pastor@pdmi.ras.ru},
abstractNote = {A graph is called cyclically 4-edge-connected if removing any three edges from it results in a graph in which at most one connected component contains a cycle. A 3-connected graph is 4-edge-connected if and only if removing any three edges from it results in either a connected graph or a graph with exactly two connected components one of which is a single-vertex one. We show how to associate with any 3-connected graph a tree of components such that every component is a 3-connected and cyclically 4-edge-connected graph.},
doi = {10.1007/S10958-018-3859-0},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 1,
volume = 232,
place = {United States},
year = {2018},
month = {7}
}