A Characterization of weakly four-connected graphs

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Abstract

A graph G = (V, E) is called weakly four-connected if G is 4-edge-connected and G - x is 2-edge-connected for all x ∈ V. We give sufficient conditions for the existence of 'splittable' vertices of degree four in weakly four-connected graphs. By using these results we prove that every minimally weakly four-connected graph on at least four vertices contains at least three 'splittable' vertices of degree four, which gives rise to an inductive construction of weakly four-connected graphs. Our results can also be applied in the problem of finding 2-connected orientations of graphs.

Original languageEnglish
Pages (from-to)217-229
Number of pages13
JournalJournal of Graph Theory
Volume52
Issue number3
DOIs
Publication statusPublished - Jul 1 2006

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Keywords

  • Connectivity of graphs
  • Edge splitting
  • Weakly four-connected

ASJC Scopus subject areas

  • Geometry and Topology

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