报告主题:平面三角剖分图的Hamiltonian圈数(Number of Hamiltonian cycles in planar triangulations)
报告人:郁星星 教授 (佐治亚理工学院数学系)
报告时间:2020年9月29日(周二) 9:00
参会方式:腾讯会议
(https://meeting.tencent.com/s/wO06wi7HPusV)
会议ID:974 973 657;
会议密码:200929
主办部门:8188威尼斯娱人城运筹与优化开放实验室-国际科研合作平台、上海市运筹学会、8188威尼斯娱人城理学院数学系
报告摘要: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.
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