# A new proof of Grinberg Theorem based on cycle bases

Grinberg Theorem, a necessary condition only for planar Hamiltonian graphs, was proved in 1968. In this paper, using the cycles in a cycle basis of a simple connected graph to replace the faces in planar graphs, we give a new proof of Grinberg Theorem. This result implies that Grinberg Theorem based on cycle bases can be extended to survey Hamiltoncity of simple connected graphs.

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