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math.CO2022★ 1 cited
Few hamiltonian cycles in graphs with one or two vertex degrees
Jan Goedgebeur, Jorik Jooken, On-Hei Solomon Lo +2
We fully disprove a conjecture of Haythorpe on the minimum number of hamiltonian cycles in regular hamiltonian graphs, thereby extending a result of Zamfirescu, as well as correct…
math.CO2022★ 1 cited
Counting cycles in planar triangulations
On-Hei Solomon Lo, Carol T. Zamfirescu
We investigate the minimum number of cycles of specified lengths in planar -vertex triangulations . It is proven that this number is for any cycle length at most $3 +…