On the existence of k edge-disjoint 2-connected spanning subgraphs

Research output: Article

15 Citations (Scopus)

Abstract

We prove that every 6k-connected graph contains k edge-disjoint rigid (and hence 2-connected) spanning subgraphs. By using this result we can settle special cases of two conjectures, due to Kriesell and Thomassen, respectively: we show that every 12-connected graph G has a spanning tree T for which G - E(T) is 2-connected, and that every 18-connected graph has a 2-connected orientation.

Original languageEnglish
Pages (from-to)257-262
Number of pages6
JournalJournal of Combinatorial Theory. Series B
Volume95
Issue number2
DOIs
Publication statusPublished - nov. 2005

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Spanning Subgraph
Connected graph
Disjoint
Spanning tree

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

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title = "On the existence of k edge-disjoint 2-connected spanning subgraphs",
abstract = "We prove that every 6k-connected graph contains k edge-disjoint rigid (and hence 2-connected) spanning subgraphs. By using this result we can settle special cases of two conjectures, due to Kriesell and Thomassen, respectively: we show that every 12-connected graph G has a spanning tree T for which G - E(T) is 2-connected, and that every 18-connected graph has a 2-connected orientation.",
keywords = "2-connected orientation, Connectivity of graphs, Rigidity matroid",
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AB - We prove that every 6k-connected graph contains k edge-disjoint rigid (and hence 2-connected) spanning subgraphs. By using this result we can settle special cases of two conjectures, due to Kriesell and Thomassen, respectively: we show that every 12-connected graph G has a spanning tree T for which G - E(T) is 2-connected, and that every 18-connected graph has a 2-connected orientation.

KW - 2-connected orientation

KW - Connectivity of graphs

KW - Rigidity matroid

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