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math.CO2021★ 2 cited
On graphs with unique geoodesics and antipodes
Dmitriy Gorovoy, David Zmiaikou
In 1962, Oystein Ore asked in which graphs there is exactly one geodesic between any two vertices. He called such graphs geodetic. In this paper, we systematically study properties…
math.CO2010
On a conjecture of H. Gupta
Emmanuel Lecouturier, David Zmiaikou
Denote by r(n) the length of a shortest integer sequence on a circle containing all permutations of the set {1,2,...,n} as subsequences. Hansraj Gupta conjectured in 1981 that r(n)…