Abstract
Hakimi, Schmeichel and Thomassen showed in 1979 that every 4-connected triangulation on n vertices has at least n∕log2n hamiltonian cycles, and conjectured that the sharp lower bound is 2(n−2)(n−4). Recently, Brinkmann, Souffriau and Van Cleemput gave an improved lower bound 125(n−2). In this paper we show that every 4-connected triangulation with O(logn) 4-separators has Ω(n2∕log2n) hamiltonian cycles.
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