On Removable and Non-Separating Even Cycles in Graphs

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Authors

  • Department of Mathematics, University of Pune, Pune 411007 ,IN
  • Department of Mathematics, University of Pune, Pune 411007 ,IN

Keywords:

2-Connected Graph, Even Cycle.

Abstract

Conlon proved that there exists an even cycle C in a 3-connected graph ≅K5, of minimum degree at least 4 such that G-E(C) is 2-connected and G - V(C) is connected. We prove that a 2-connected graph G of minimum degree at least 5 has an even cycle C such that G - E(C) is 2-connected and G - V(C) is connected.