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Hamiltonian cycles and 1-factors in 5-regular graphs
[article]
2021
arXiv
pre-print
It is proven that for any integer g ≥ 0 and k ∈{ 0, ..., 10 }, there exist infinitely many 5-regular graphs of genus g containing a 1-factorisation with exactly k pairs of 1-factors that are perfect, i.e. form a hamiltonian cycle. For g = 0, this settles a problem of Kotzig from 1964. Motivated by Kotzig and Labelle's "marriage" operation, we discuss two gluing techniques aimed at producing graphs of high cyclic edge-connectivity. We prove that there exist infinitely many planar 5-connected
arXiv:2008.03173v2
fatcat:5cyupj3qcreenc7y6hbss4nowe