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arXiv · 0704.0309

The Complexity of HCP in Digraps with Degree Bound Two

Guohun Zhu
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Abstract

The Hamiltonian cycle problem (HCP) in digraphs D with degree bound two is solved by two mappings in this paper. The first bijection is between an incidence matrix C_{nm} of simple digraph and an incidence matrix F of balanced bipartite undirected graph G; The second mapping is from a perfect matching of G to a cycle of D. It proves that the complexity of HCP in D is polynomial, and finding a second non-isomorphism Hamiltonian cycle from a given Hamiltonian digraph with degree bound two is also polynomial. Lastly it deduces P=NP base on the results.

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Guohun Zhu. 2007-07-13. The Complexity of HCP in Digraps with Degree Bound Two. https://arxiv.org/abs/0704.0309

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