Graphs and Combinatorics

, Volume 3, Issue 1, pp 285–291 | Cite as

On thel-connectivity of a graph

  • Ortrud R. Oellermann
Article

Abstract

For an integerl ≥ 2, thel-connectivity of a graphG is the minimum number of vertices whose removal fromG produces a disconnected graph with at leastl components or a graph with fewer thanl vertices. A graphG is (n, l)-connected if itsl-connectivity is at leastn. Several sufficient conditions for a graph to be (n, l)-connected are established. IfS is a set ofl(≥ 3) vertices of a graphG, then anS-path ofG is a path between distinct vertices ofS that contains no other vertices ofS. TwoS-paths are said to be internally disjoint if they have no vertices in common, except possibly end-vertices. For a given setS ofl ≥ 2 vertices of a graphG, a sufficient condition forG to contain at leastn internally disjointS-paths, each of length at most 2, is established.

Keywords

Distinct Vertex Condition forG 

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Ortrud R. Oellermann
    • 1
  1. 1.Department of MathematicsWestern Michigan UniversityKalamazooUSA

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