介绍
I was born in Taipei Taiwan, where I got my BS degree in 数学. 在那待了两年之后 中国科学院数学研究所 in Taiwan as a research assistant, I came to the US for my Ph.D. 在 南卡罗来纳大学哥伦比亚分校 在…的监督下 杰瑞Griggs.
Ever since joined the 加州大学洛杉矶分校 faculty in 1991, I have been pursuing both my teaching and research goals. I am extremely honored to be the recipient of the 2015 MAA (数学ematical Association of America) Southern California and Nevada Sectional Distinguished Teaching Award，同时也是 足彩外围网站杰出教授奖 (2003), and Distinguished Women Award (2016) and 校长杰出教授奖 (2018).
教学的兴趣
教书是一份充实而有回报的工作! 看我的学生学习, 对这个主题感兴趣, and make achievements is the best rewards for a teacher.
在过去的几年里, I have taught more than two dozen math courses ranging from collage algebra to graduate courses. 几年前，我创建了一个高级部门 图论 课程，现在每年提供一次. 除了, I have taught several graduate seminar courses on special topics, and mentored many student research projects for both undergraduate and graduate students.
I am also interested in incorporating effective teaching strategies into my classes to enhance student learning. 目前, I am working on a flipped classroom grant (jointly with faculty from several Cal State campuses) funded by the US Department of Education.
研究
My research interests are in 图论 and combinatorics. I have been working on the following topics:
- Graph coloring parameters of distance graphs and relations to number theory problems:相关色数, 分数色数, and circular chromatic number of distance graphs to the "density of integral sets with missing differences" and the parameter involved in the so called "lonely runner conjecture," and applying these connections to solving open problems in respective areas.
- Graph labelings motivated by the channel assignment problem: Radio labeling, backbone coloring, distance two labeling, circular distance two labeling, etc.
- 应用拓扑(塔克引理), Ky Fan引理, Borsuk-Ulam Theorem etc) to study graph coloring problems.
- 图着色:顶点着色, 圆形的着色, 部分颜色, list-coloring, 强edge-coloring, 以及图形的在线上色.
目前, my research is partially supported by the 国家科学基金会 (NSF)下的一项拨款 图着色和可选择性" (2016-2019), and I am a faulty mentor for the NASA CSULA直接干 格兰特(2015 - 2020).
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D. 本特瓦和D. 刘, ``Radio Number for the Cartesian Product of Two Trees,'' 离散应用数学, 342 (2024), 304 -- 316.
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A. 查韦斯,P. 勒,D. 林,D. 刘、M. Shurman, ``Antimagic Labeling for Unions 的图 with Many 3-Paths," 离散数学, 346 (2023), 113356.
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J. Sierra和D. 刘,我. 《足彩外围网站》， 泵J. 本科生研究, 6 (2023), 268 -- 279.
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D. 刘、V. Lossada, ``An inductive approach to strongly antimagic labeling of graphs", 印度离散数学杂志, 8 (2022), 113 -- 138.
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D. 林、D. 刘, ``Antimagic and strongly antimagic labelings of jellyfish graphs union many 3-paths", 提交, 2023.
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C. 布卢姆菲尔德,D. 刘和J. Ramirez，“radio -k- labels for Large k”， 离散应用数学, 316 (2022), 60 -- 70.
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F. 常 W. 李,D. 刘、Z. Pan, ``On $k$-Shifted Antimagic Spider Forests,'' 提交, 2023.
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D. 本特瓦和D. 刘, ``Radio Number for Block 图 and Line 图 of Trees," 理论计算机科学杂志，卷891 (2021)，90-104.
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A. 查韦斯,维. 刘、M. Shurman, ``Optimal Radio-$k$-Labeling for Trees," 欧洲组合学杂志，卷91(2021)，130203,13页.
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A. 查韦斯,维. 刘、G. Robinson, ``Distance 图 Generated by Five Primes," Proceeding for the Research Symposium of the Association of Women in 数学ematics， Springer, Springer(2020)，第45—64页.
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刘和格兰特·罗宾逊， Integral sequences with three missing separations. 欧洲组合学杂志, 85 (2020), 103056, 11 pp.
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Y. 江,D. 刘,Y.-N. 是的，还有X. 朱, ``Colouring of Generalized Signed Triangle-Free Planar 图," 离散数学 342 (2019), 836--843.
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Z. 胡,K.-W. 李，刘， Upper Bounds on the Strong Chromatic Index of Halin 图. 数学图论中的讨论, 38 (2018), 5--26.
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刘, Strong Chromatic Index of Regular Puffer 图,手稿.
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刘和X. 朱, A Combinatoria "l Proof for the Circular Chromatic Number of Kneser 图, J. Combin. 优化, 32 (2016), no. 3, 765–-774. .
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Y. 但是,年代. 芬博，刘和X. 朱, 列出图的主色, 离散应用数学, 167 (2014), 45 -- 51.
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Daniel Collister和刘， D = {2,3, x, y}时K(D)的研究. J. Kratochvil, M. 米勒和D. Froncek(编辑). 组合算法. 计算机科学课堂讲稿，Springer. Proceeding of the 25th International Workshop, IWOCA 2014 Duluth, MN, USA, 2015, 250 -- 261.
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D. 刘和A. Sutedja, Chromatic Number of Distance 图 Generated by the Sets {2, 3, x, y}, J. 组合优化, 25 (2013), 680 -- 693.
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Y. 但是，刘和X. 朱, Backbone Coloring for 图 with Large Girths, 离散数学, 313 (2013), 1799 -- 1804.
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G. J. 张，刘，和X. 朱, A Short Proof for Chen's Alternative Kneser Coloring Theorem, J. 《组合理论A辑. 120 (2013), 159 -- 163.
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G. J. 张和刘， 三次Halin图的强边着色, 离散数学, 312 (2012), 1468 -- 1475.
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J. 娟和刘， 环的对映标记, 农业研究所 Combinatoria " ", 103 (2012), 81 -- 86.
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S.-J. 金,Y. 权，刘和X. 朱, On-line List Colouring of Complete Multipartite 图, 电子J. 组合， 19(2012)，论文41,13页.
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K.-W. 李和刘， On the Strong Chromatic Index of Cubic Halin 图, 应用数学. 信, 25 (2012), 898 -- 901.
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刘，诺琳，潘和X. 朱, Circular Consecutive Choosibility for k-Choosable 图, J. 图论, 67 (2011), 178 -- 197.
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D. 刘, 树的哈密顿谱, 农业研究所 Combinatoria " ", 99 (2011), 415 -- 419.
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W. 林，刘和X. 朱, 图的Mycielskian的多重着色, J. 图论, 63 (2010), 311 -- 323.
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J. Juan, 刘和L. 陈, L(j, k)-树的标记, 圆盘应用数学, 158 (2010), 692 -- 698.
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刘和M. 谢, 方形路径的无线电号码, 农业研究所 Combinatoria ", 90 (2009), 307--319.
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K.-W. 李，刘和W.-F. 王, On (d,1)-图的总数, 盘数学, 309 (2009), 3767--3773.
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刘, 树木无线电编号, 阀瓣. 数学., 308 (2008), 1153--1164.
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刘, From Rainbow to the Lonely Runner: A Survey, 台湾J. 数学., 12 (2008), 851--871.
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刘和X. 朱, Fractional Chromatic Number of Distance 图 with Two Interval Distance Sets, 欧洲J. 组合, 29 (2008), 1733--1743.
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刘和 X. 朱, The Circular Distance Two Labeling and the L(2, 1)-Number for Outerplanar 图, 暹罗J. 离散数学, 19 (2005), 281--293.
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刘和 X. 朱, Fractional Chromatic Number and Circular Chromatic Number for Distance 图 with Large Clique Size, J. 图论, 47 (2004), 129--146. 勘误表, J. 图论, 48 (2005), 329--330.
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刘和 X. 朱, Multi-level Distance Labelings and Radio Number for Paths and Cycles, 暹罗J. 离散数学, 19 (2005), 610--621.
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刘, Circular Chromatic Number of Iterated Mycielski 图, 离散数学, 285 (2004), 335--334.
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刘和M. 谢, 循环平方的无线电数, Congressus Numerantium, 169 (2004), 105--125.
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刘和 X. 朱, 圆距离两个标签 和圆形色数, 农业研究所 Combinatoria " ", 69 (2003), 177--183.
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刘, On sizes 的图 with Fixed Orders and Spans of Circular Distance Two Labellings, 农业研究所 Combinatoria " ", 67 (2003), 125--139.
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K.-W. Lih 和刘 Circular Chromatic Number of some Reduced Kneser 图, J. 图论, 41 (2002), 62--68.
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刘和 X. 朱, Asymptotic Clique Covering Ratio of Distance 图, 欧洲J. 组合, 23 (2002), 315--327.
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G. J. 常, S. 胡安和D. 刘, Minimum Span of No-hole (r+1)-Distant Coloring, 暹罗J. 离散数学, 14 (2001), 370--380.
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刘, Hamiltonicity and Path Covering to Distance Two Labellings 的图, 离散数学, 232 (2001), 163--169.
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G. J. 常, S. 胡安和D. 刘, No-Hole 2-Distant Coloring for Unit Interval 图, 农业研究所 Combinatoria " ", 61 (2001), 233--244.
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G. J. 常, W. 柯,D. 郭，刘和 R. 叶, 论L(d,1)-图的标注, 离散数学, 220 (2000), 57--66.
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刘, Chromatic Number of Distance 图 and the Channel Assignment Problem, 农业研究所 Combinatoria " ", 56 (2000), 65--80.
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G. J. 常, D. 刘和 X. 朱, 距离图和t着色, J. 组合理论系列B， 75 (1999), 259--269.
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刘和 X. 朱, Distance 图 with Missing Multiples in the Distance Sets, J. 图论, 30 (1999), 245--259.
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刘和 R. 叶, Minimup Span of No-hole T-coloring 的图, Congressus Numerantium, 138 (1999), 39--48.
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刘和 R. 叶，足彩外围网站图的距离二标注， 农业研究所 Combinatoria " ", 47 (1997), 13--22.
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刘, T-图 and the Channel Assignment Problem, 离散数学, 161 (1996), 197--205.
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J. Griggs 和刘 Channel Assignment Problem for Mutually Adjacent Sites, J. 《组合理论A辑, 68 (1994), 169--183.
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足彩外围网站t -着色的一个猜想, Congressus Numerantium, 103 (1994), 27--31.
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图的t -着色, 离散数学, 101 (1992), 203--211.
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刘, Graph homomorphism and the channel assignment problem, Ph.D. Dissertation, 南卡罗来纳大学哥伦比亚分校, 1991.
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K-W. Lih 和刘 帕斯卡的标记和路径计数,手稿.
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刘, Circular Coloring for 图 with Distance Constraints,手稿.
在建设中
在建设中
教育背景
Ph.D. 数学. 1991
- 南卡罗来纳大学哥伦比亚分校.
- 指导老师:Jerrold R. Griggs. Dissertation Title: Graph Homomorphism and the Channel Assignment Problem.
B.S. 数学. 1985
- 台湾国立中央大学.