時(shí)間：2023年6月14日 星期三 9:00-11:00
地點(diǎn)：東校區(qū)二教203
報(bào)告題目：The s-hamiltonian line graph problem
報(bào)告人：賴(lài)虹建教授
邀請(qǐng)人：游志福
報(bào)告摘要：Thomassen posed the conjecture that every 4-connected line graph is hamiltonian in 1984. Matthews-Sumner conjectured that every 4-connected claw-free graph is hamiltonian. In 1999, Ryjachek introduced the line graph closure of a claw-free graph and showed that the two conjectures above are equivalent. In 2004, Kuczel and L. Xiong further conjectured that every 4-connected line graph is hamiltonian-connected, and in 2011, Ryjachek and Vrana conjectured that every 4-connected claw-free graph is hamiltonian connected, and showed that all 4 conjectures presented above are equivalent. All these conjectures are sufficient conditions. In 1987, Broersma and Veldman raised the problem to investigate necessary and sufficient conditions for a line graph to be s-hamiltonian. In this talk, we will present our considerations of seeking necessary and sufficient condition version of the Thomassen conjecture in the format of the s-hamiltonian line graphs and claw-free graphs, and the related developments and progresses.
報(bào)告人簡(jiǎn)介：美國(guó)西弗吉尼亞大學(xué)數(shù)學(xué)系終身教授，博士生導(dǎo)師，國(guó)際知名的圖論專(zhuān)家，主要研究領(lǐng)域包括圖論中的歐拉子圖、哈密爾頓性問(wèn)題、整數(shù)流以及圖論中的染色和連通度問(wèn)題，出版學(xué)術(shù)著作兩部，發(fā)表學(xué)術(shù)論文250余篇。完成了兩部專(zhuān)著：由克魯亞學(xué)術(shù)出版社（Kluwer Academic Publishing）出版的“圖與組合學(xué)中的矩陣論”和由高等教育出版社出版的“擬陣論”。1996年獲學(xué)院最優(yōu)科研獎(jiǎng)，2006年獲學(xué)院最優(yōu)教師獎(jiǎng)和全校最優(yōu)教師獎(jiǎng)，成為西弗吉尼亞大學(xué)歷史上第一個(gè)獲此榮譽(yù)的華裔教授。曾主持過(guò)1996年由美國(guó)國(guó)家自然科學(xué)基金會(huì)資助的紀(jì)念凱特林（Catlin）教授的歐拉圖問(wèn)題專(zhuān)題會(huì)議，2008年由美國(guó)國(guó)家自然科學(xué)基金會(huì)資助的第46屆美國(guó)中西部圖論會(huì)議，以及2018年的第59屆美國(guó)中西部圖論會(huì)議。曾任Discrete Mathematics雜志客座編輯，現(xiàn)擔(dān)任Applied Mathematics和Graphs and Combinatorics等多個(gè)雜志的編輯。
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