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        數學系Seminar第2010期 平面三角剖分圖的Hamiltonian圈數

        創建時間:  2020/09/24  龔惠英   瀏覽次數:   返回

                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

        https://meeting.tencent.com/s/wO06wi7HPusV

        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!

        上一條:前沿新材料系列報告 Li-ion battery and beyond

        下一條:數學系Seminar第2009期 可壓縮歐拉方程組大解的最新進展


        數學系Seminar第2010期 平面三角剖分圖的Hamiltonian圈數

        創建時間:  2020/09/24  龔惠英   瀏覽次數:   返回

                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

        https://meeting.tencent.com/s/wO06wi7HPusV

        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!

        上一條:前沿新材料系列報告 Li-ion battery and beyond

        下一條:數學系Seminar第2009期 可壓縮歐拉方程組大解的最新進展

        江苏快三计划