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The prism over a graph G is the Cartesian product G2K 2 of G with the complete graph K 2. If G is hamiltonian, then G2K 2 is also hamiltonian but the converse does not hold in general. Having a hamiltonian prism is shown to be an interesting relaxation of being hamiltonian. In this paper, we examine classical problems on hamiltonicity of graphs in the… (More)

Let G be the class of simple planar graphs of minimum degree ≥ 4 in which no two vertices of degree 4 are adjacent. A graph H is light in G if there is a constant w such that every graph in G which has a subgraph isomorphic to H also has a subgraph isomorphic to H whose sum of degrees in G is ≤ w. Then we also write w(H) ≤ w. It is proved that the cycle C s… (More)