講座主題：On equitable tree-colorings of graphs
主講人： 張欣
工作單位：西安電子科技大學
講座時間：2019年6月27日10:00
講座地點：數學院大會議室
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
An equitable tree-$k$-coloring of a graph is a vertex coloring using $k$ distinct colors such that every color class induces a forest and the sizes of any two color classes differ by at most one. The minimum integer $k$ such that a graph $G$ is equitably tree-$k$-colorable is the equitable vertex arboricity of $G$, denoted by $va_{eq}(G)$. A graph that is equitably tree-$k$-colorable may admits no equitable tree-$k'$-coloring for some $k'>k$. For example, the complete bipartite graph $K_{9,9}$ has an equitable tree-$2$-coloring but is not equitably tree-3-colorable. In view of this a new chromatic parameter so-called the equitable vertex arborable threshold is introduced. Precisely, it is the minimum integer $k$ such that $G$ has an equitable tree-$k'$-coloring for any integer $k'\geq k$, and is denoted by $va_{eq}^*(G)$. The concepts of the equitable vertex arboricity and the equitable vertex arborable threshold were introduced by J.-L. Wu, X. Zhang and H. Li in 2013. In 2016, X. Zhang also introduced the list analogue of the equitable tree-$k$-coloring. There are many interesting conjectures on the equitable (list) tree-colorings, one of which, for example, conjectures that every graph with maximum degree at most $\Delta$ is equitably tree-$k$-colorable for any integer $k\geq (\Delta+1)/2$, i.e, $va_{eq}^*(G)\leq \lceil(\Delta+1)/2\rceil$. In this talk, I review the recent progresses on the studies of the equitable tree-colorings from theoretical results to practical algorithms, and also share some interesting problems for further research.
主講人介紹：
張欣，2007年7月畢業于山東大學數學與系統科學學院，獲得理學學士學位，同年9月，進入山東大學數學學院攻讀博士學位，師從吳建良教授（碩士階段）與劉桂真教授（博士階段），于2012年6月畢業并獲得理學博士學位，現任西安電子科技大學數學與統計學院副教授、碩士研究生導師，主要從事圖論及其應用方向的科研教學工作，研究興趣包括圖（網絡）的拓撲結構與染色（劃分），信息編碼理論等，現發表SCI檢索學術論文60余篇，主持國家自然科學基金面上基金項目與青年科學基金項目各一項，高等學校博士學科點專項科研基金一項，陜西省自然科學基礎研究計劃面上項目與青年人才項目各一項，入選西安市科協青年人才托舉計劃，曾獲得山東省優秀博士學位論文獎，陜西高等學校科學技術獎二等獎，中國運籌學會青年科技獎等多項科研獎勵，現為《Journal of Combinatorial Theory, Series B》、《Journal of Graph Theory》、《Discrete Applied Mathematics》、《Discrete Mathematics》、《Graphs and Combinatorics》、《數學學報（英文版）》等國際期刊的審稿人，美國數學會《Mathematical Reviews》評論員，中國運籌學會圖論組合分會青年理事，中國工業與應用數學學會圖論組合及應用專業委員會委員。
