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      【7月26日】組合數學及其應用創新團隊系列報告

      發布時間:2020-07-20文章來源:劉麗 瀏覽次數:

      2020年組合數學及其應用創新團隊系列報告

      報告時間:2020726日上午8:30-11:30

      報告地點:騰訊會議833495161

      報告題目:Rainbow Independent Sets in Cycles

      報告摘要:For a given class C of graphs and given integers m \le n, let f_ C(n,m) be the minimal number k such that every k independent n-sets in any graph belonging to C have a (possibly partial) rainbow independent m-set. In this talk, I will give our result about rainbow independent sets on the case C=C_{2s+1}. Our result is a special case of the conjecture (Conjecture 2.9) proposed by Aharoni et al in \cite{Aharoni}. This talk is based on the work jointed with Zequn Lv.

      報告人:陸玫教授,博士生導師。 19937月在中國科學院數學與系統科學研究院獲博士學位足彩app_首页,現為清華大學數學科學系教授,博士生導師,主要從事運籌學、圖論與組合優化方面的研究,在《Journal of Combinatorial Theory, Series B》足彩app_首页、 《Journal of Graph Theory》、 《Linear Algebra and Applications》、《Discrete Applied Mathematics》、《Discrete Mathematics》、《Journal of Combinatorial Optimization》等國際權威學術期刊發表SCI檢索論文60余篇?,F任清華大學數學科學系計算數學與運籌學研究所所長,中國運籌學會圖論組合分會副理事長,中國工業與應用數學學會圖論組合及應用專業委員會秘書長,中國組合數學與圖論學會理事。

      報告題目:Graph Densities and Fractional Edge-Colorings

      報告摘要:Given a multigraph G=(V,E) with a positive rational weight w(e) on each edge e, the weighted density problem (WDP) is to find a subset U of V, with |U|\ge 3 and odd, that maximizes \frac{2w(U)}{|U|-1}, where w(U) is the total weight of all edges with both ends in U, and the weighted fractional edge-coloring problem (WFECP) can be formulated as the linear program Minimize Subject to where A is the edge-matching incidence matrix of G. These two problems are closely related to the celebrated

      Goldberg-Seymour conjecture on edge-colorings of multigraphs, and have great interests in their own rights. Even when w(e) = 1 for all edges e, determining whether WDP can be solved in polynomial time was posed by Jensen and Toft [Topics in Chromatic Graph Theory, Cambridge University Press, Cambridge, 2015, pp. 327--357] and by Stiebitz et al. [Graph Edge Colouring: Vizing's Theorem and Goldberg's Conjecture, John Wiley, New York, 2012] as an open problem. We design strongly polynomial-time algorithms for solving WDP and WFECP exactly, and develop a novel matching removal technique for multigraph edge-coloring. (Joint work with Wenan Zang, Qiulan Zhao.)

      報告人:陳旭瑾研究員,博士生導師。2000年東南大學應用數學系獲碩士學位, 2004年香港大學數學系獲博士學位,現為中國科學院數學與系統科學研究院研究員。從事運籌學及相關領域的研究工作,主要研究興趣和方向是組合優化的理論和應用,包括算法博弈論、網絡優化、多面體組合等。2010年獲中國運籌學會青年科技獎一等獎,2013年獲首屆國家優秀青年基金足彩app_首页。

      報告題目:Degree sums and dominating cycles

      報告摘要:A cycle C of a graph G is dominating if any vertex of V(G)\V(C) has at least one neighbor on C and V(G)\V(C) is an independent set. Let G be a k-connected graph of order n≥3 with k≥2. In this talk, we will introduce our new result that every longest cycle of G is dominating if the degree sums is more than (k+1)(n+1)/3 for any k+1 pairwise nonadjacent vertices, and the lower bound is sharp, which generalizes the results due to Bondy for k=2 and Lu et al. for k=3.

      報告人:陳耀俊教授,博士生導師。20007月在中國科學院數學與系統科學研究院獲理學博士學位;2000.7-2002.6在南京大學數學系從事博士后研究工作足彩app_首页;2003.9-2005.8在香港理工大學商學院物流系從事博士后研究工作;目前主要從事圖中特定子圖結構、Ramsey 數以及編碼理論足彩app_首页、理論計算機與組合圖論交叉問題的研究足彩app_首页。近些年主持國家自然科學基金多項,在國內外專業學術雜志上發表多篇研究論文足彩app_首页,其中50余篇發表在SCI檢索源期刊上。

      報告題目:On the normalized Laplacian spectra of graphs

      報告摘要In this talk, we introduce some properties of normalized Laplacian spectra of graphs. In particular, we prove that the generalized friendship graph  which is a graph on  vertices obtained by joining a vertex to all vertices of  disjoint copy of complete graph  on  vertices, is determined by its normalized Laplacian spectrum for ,while  is not determined by its normalized Laplacian spectra for . We conclude a conjecture on the normalized Laplacian spectra.

      報告人:張曉東教授,博士生導師。19986月在中國科學技術大學獲得理學博士學位。曾在以色列理工學院(得到Lady Davis Postdoctoral fellowship 資助)和智利大學做博士后、美國加州大學圣地亞哥分校等校做訪問學者。多次主持國家自然科學基金項目和參加國家973項目和863項目。曾獲得安徽省科技進步二等獎和教育部科學技術進步三等獎足彩app_首页。 已經在SCI期刊發表120多篇論文,出版專著一本;曾在華人數學家大會上作邀請報告;擔任中國運籌學會圖論組合分會副理事長。目前主要研究領域為譜圖理論足彩app_首页,隨機圖與復雜網絡,組合矩陣論等。



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