# Immersions in highly edge connected graphs

Marx, Dániel and Wollan, P
(2014)
*Immersions in highly edge connected graphs.*
SIAM JOURNAL ON DISCRETE MATHEMATICS, 28 (1).
pp. 503-520.
ISSN 0895-4801
10.1137/130924056

Text
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## Abstract

We consider the problem of how much edge connectivity is necessary to force a graph G to contain a fixed graph H as an immersion. We show that if the maximum degree in H is δ, then all the examples of δ-edge connected graphs which do not contain H as a weak immersion must have a treelike decomposition called a tree-cut decomposition of bounded width. If we consider strong immersions, then it is easy to see that there are arbitrarily highly edge connected graphs which do not contain a fixed clique Kt as a strong immersion. We give a structure theorem which roughly characterizes those highly edge connected graphs which do not contain Kt as a strong immersion. © 2014 Society for Industrial and Applied Mathematics.

Item Type: | Article |
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Uncontrolled Keywords: | Graph theory; Tree-like decomposition; Maximum degree; Graph G; Fixed graphs; Connected graph; Forestry; Tree-cut decomposition; IMMERSIONS; Edge connectivity |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Divisions: | Informatics Laboratory |

SWORD Depositor: | MTMT Injector |

Depositing User: | MTMT Injector |

Date Deposited: | 26 Sep 2014 19:20 |

Last Modified: | 26 Sep 2014 19:20 |

URI: | https://eprints.sztaki.hu/id/eprint/8004 |

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