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 數學系 Seminar 第 2010期     上海大學運籌與優化開放實驗室國際科研合作平臺系列報告 報告主題：平面三角剖分圖的Hamiltonian圈數（Number of Hamiltonian cycles in planar triangulations） 報告人：郁星星 教授 （佐治亞理工學院數學系） 報告時間：2020年9月29日（周二） 9:00 參會方式：騰訊會議 會議ID：974 973 657；會議密碼：200929 主辦部門：上海大學運籌與優化開放實驗室-國際科研合作平臺、上海市運籌學會、上海大學理學院數學系 報告摘要：Whitney proved in 1931 that 4-connected planar triangulations are Hamiltonian. Hakimi, Schmeichel, and Thomassen conjectured in 1979 that if $G$ is a 4-connected planar triangulation with $n$ vertices then $G$ contains at least $2(n-2)(n-4)$ Hamiltonian cycles, with equality if and only if $G$ is a double wheel. We show that if $G$ has $O(n/{\log}_2 n)$ separating 4-cycles then $G$ has $\Omega(n^2)$ Hamiltonian cycles, and if $\delta(G)\ge 5$ then $G$ has $2^{\Omega(n^{1/4})}$ Hamiltonian cycles. Both results improve previous work. Moreover, the proofs involve a “double wheel” structure, providing further evidence to the above conjecture. Joint work with Xiaonan Liu. 歡迎教師、學生參加！
 數學系 Seminar 第 2010期     上海大學運籌與優化開放實驗室國際科研合作平臺系列報告 報告主題：平面三角剖分圖的Hamiltonian圈數（Number of Hamiltonian cycles in planar triangulations） 報告人：郁星星 教授 （佐治亞理工學院數學系） 報告時間：2020年9月29日（周二） 9:00 參會方式：騰訊會議 會議ID：974 973 657；會議密碼：200929 主辦部門：上海大學運籌與優化開放實驗室-國際科研合作平臺、上海市運籌學會、上海大學理學院數學系 報告摘要：Whitney proved in 1931 that 4-connected planar triangulations are Hamiltonian. Hakimi, Schmeichel, and Thomassen conjectured in 1979 that if $G$ is a 4-connected planar triangulation with $n$ vertices then $G$ contains at least $2(n-2)(n-4)$ Hamiltonian cycles, with equality if and only if $G$ is a double wheel. We show that if $G$ has $O(n/{\log}_2 n)$ separating 4-cycles then $G$ has $\Omega(n^2)$ Hamiltonian cycles, and if $\delta(G)\ge 5$ then $G$ has $2^{\Omega(n^{1/4})}$ Hamiltonian cycles. Both results improve previous work. Moreover, the proofs involve a “double wheel” structure, providing further evidence to the above conjecture. Joint work with Xiaonan Liu. 歡迎教師、學生參加！