The Journal of the Indian Mathematical Society

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On Removable and Non-Separating Even Cycles in Graphs


Affiliations
1 Department of Mathematics, University of Pune, Pune 411007, India
     

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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.

Keywords

2-Connected Graph, Even Cycle.
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  • On Removable and Non-Separating Even Cycles in Graphs

Abstract Views: 209  |  PDF Views: 0

Authors

Y. M. Borse
Department of Mathematics, University of Pune, Pune 411007, India
B. N. Waphare
Department of Mathematics, University of Pune, Pune 411007, India

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.

Keywords


2-Connected Graph, Even Cycle.