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(xué)
講座時(shí)間：2019年6月27日10:00
講座地點(diǎn)：數(shù)學(xué)院大會議室
主辦單位：煙臺大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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(yè)于山東大學(xué)數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院，獲得理學(xué)學(xué)士學(xué)位，同年9月，進(jìn)入山東大學(xué)數(shù)學(xué)學(xué)院攻讀博士學(xué)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(yè)并獲得理學(xué)博士學(xué)位，現(xiàn)任西安電子科技大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院副教授、碩士研究生導(dǎo)師，主要從事圖論及其應(yīng)用方向的科研教學(xué)工作，研究興趣包括圖（網(wǎng)絡(luò)）的拓?fù)浣Y(jié)構(gòu)與染色（劃分），信息編碼理論等，現(xiàn)發(fā)表SCI檢索學(xué)術(shù)論文60余篇，主持國家自然科學(xué)基金面上基金項(xiàng)目與青年科學(xué)基金項(xiàng)目各一項(xiàng)，高等學(xué)校博士學(xué)科點(diǎn)專項(xiàng)科研基金一項(xiàng)，陜西省自然科學(xué)基礎(chǔ)研究計(jì)劃面上項(xiàng)目與青年人才項(xiàng)目各一項(xiàng)，入選西安市科協(xié)青年人才托舉計(jì)劃，曾獲得山東省優(yōu)秀博士學(xué)位論文獎(jiǎng)，陜西高等學(xué)校科學(xué)技術(shù)獎(jiǎng)二等獎(jiǎng)，中國運(yùn)籌學(xué)會青年科技獎(jiǎng)等多項(xiàng)科研獎(jiǎng)勵(lì)，現(xiàn)為《Journal of Combinatorial Theory, Series B》、《Journal of Graph Theory》、《Discrete Applied Mathematics》、《Discrete Mathematics》、《Graphs and Combinatorics》、《數(shù)學(xué)學(xué)報(bào)（英文版）》等國際期刊的審稿人，美國數(shù)學(xué)會《Mathematical Reviews》評論員，中國運(yùn)籌學(xué)會圖論組合分會青年理事，中國工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會圖論組合及應(yīng)用專業(yè)委員會委員。
