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Barnette's conjecture states that every three connected cubic bipartite planar graph (CPB3C) is Hamiltonian. In this paper we show the existence of a family of CPB3C Hamiltonian graphs in which large and large subgraphs are non-Hamiltonian.doi:10.2478/ausm-2019-0026 fatcat:lnnlgxiknfesfptvhx6gjsy3fa