Necessary Condition for Cubic Planer three Connected Graph to be Non- Hamiltonian and proof of Barnettes Conjecture

Abstract

A conjecture of Barnette's states that every three connected cubic bipartite planer graph is Hamiltonian. This problem has remained open since its formulation .This paper has a threefold purpose. The first is to provide survey of literature surrounding the conjecture. The second is to give the necessary condition for cubic planer three connected graph to be non Hamiltonian, and finally I shall prove the Barnette's conjecture. For the proof of different results using to prove the results I illustrate most of the results by using counter examples.