INTRODUCTION
I was born in Taipei Taiwan, where I got my BS degree in Math. After spending two years at the Institute of Math, Academia Sinica in Taiwan as a research assistant, I came to the US for my Ph.D. at the University of South Carolina, Columbia under the supervision of Jerry Griggs.
Ever since joined the Cal State LA 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 (Mathematical Association of America) Southern California and Nevada Sectional Distinguished Teaching Award, as well as a recipient of the Cal State LA Outstanding Professor Award (2003), and Distinguished Women Award (2016) and President's Distinguished Professor Award (2018).
TEACHING INTERESTS
Teaching is a fulfilling and rewarding job! To see my student learn, get interested in the subject, and make achievements is the best rewards for a teacher.
During the past years, I have taught more than two dozen math courses ranging from collage algebra to graduate courses. Some years ago I created an upper division graph theory course, which is now offered annually. In addition, 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. Currently, I am working on a flipped classroom grant (jointly with faculty from several Cal State campuses) funded by the US Department of Education.
RESEARCH
My research interests are in graph theory and combinatorics. I have been working on the following topics:
- Graph coloring parameters of distance graphs and relations to number theory problems: Relating chromatic number, fractional chromatic number, 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.
- Applying topology (Tucker Lemma, Ky Fan Lemma, Borsuk-Ulam Theorem etc) to study graph coloring problems.
- Graphs colorings: Vertex coloring, circular coloring, fractional coloring, list-coloring, strong edge-coloring, and on-line coloring of graphs.
Currently, my research is partially supported by the National Science Foundation (NSF) under a grant entitled "Graph Coloring and Choosability" (2016-2019), and I am a faulty mentor for the NASA CSULA Direct STEM grant (2015-2020).
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D. Bentva, and D. Liu, ``Radio Number for the Cartesian Product of Two Trees,'' Discrete Applied Mathematics, 342 (2024), 304 -- 316.
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A. Chavez, P. Le, D. Lin, D. Liu, and M. Shurman, ``Antimagic Labeling for Unions of Graphs with Many 3-Paths," Discrete Mathematics, 346 (2023), 113356.
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J. Sierra, and D. Liu, J. Toy, ``Antimagic Labeling of Forests", PUMP J. of Undergraduate Research, 6 (2023), 268 -- 279.
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D. Liu, and V. Lossada, ``An inductive approach to strongly antimagic labeling of graphs", Indian Journal of Discrete Math, 8 (2022), 113 -- 138.
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D. Lin, and D. Liu, ``Antimagic and strongly antimagic labelings of jellyfish graphs union many 3-paths", submitted, 2023.
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C. Bloomfield, D. Liu, and J. Ramirez, ``Radio-k-Labellings for Large k," Discrete Applied Mathematics, 316 (2022), 60 -- 70.
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F. Chang, W. Li, D. Liu, and Z. Pan, ``On $k$-Shifted Antimagic Spider Forests,'' submitted, 2023.
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D. Bentva, and D. Liu, ``Radio Number for Block Graphs and Line Graphs of Trees," Journal of Theoretical Computer Science, Volume 891 (2021), 90-104.
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A. Chavez, D. Liu, and M. Shurman, ``Optimal Radio-$k$-Labeling for Trees," European Journal of Combinatorics, Vol 91 (2021), 130203, 13pp.
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A. Chavez, D. Liu, and G. Robinson, ``Distance Graphs Generated by Five Primes," Proceeding for the Research Symposium of the Association of Women in Mathematics, Springer, Springer (2020), pages 45 -- 64.
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Liu and Grant Robinson, Integral sequences with three missing separations. European Journal of Combinatorics, 85 (2020), 103056, 11 pp.
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Y. Jiang, D. Liu, Y.-N. Yeh, and X. Zhu, ``Colouring of Generalized Signed Triangle-Free Planar Graphs," Discrete Mathematics 342 (2019), 836--843.
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Z. Hu, K.-W. Lih, and Liu, Upper Bounds on the Strong Chromatic Index of Halin Graphs. Discussiones in Mathematics Graph Theory, 38 (2018), 5--26.
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Liu, Strong Chromatic Index of Regular Puffer Graphs, manuscript.
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Liu and X. Zhu, A Combinatorial Proof for the Circular Chromatic Number of Kneser Graphs, J. Combin. Optimization, 32 (2016), no. 3, 765–-774. .
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Y. Bu, S. Finbow, Liu, and X. Zhu, List Backbone Colouring of Graphs, Discrete Applied Mathematics, 167 (2014), 45 -- 51.
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Daniel Collister and Liu, Study of K(D) for D = {2, 3 , x, y}. J. Kratochvíl, M. Miller, and D. Froncek (Editors). Combinatorial Algorithms. Lecture Notes in Computer Science, Springer. Proceeding of the 25th International Workshop, IWOCA 2014 Duluth, MN, USA, 2015, 250 -- 261.
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D. Liu and A. Sutedja, Chromatic Number of Distance Graphs Generated by the Sets {2, 3, x, y}, J. Combinatorial Optimization, 25 (2013), 680 -- 693.
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Y. Bu, Liu, and X. Zhu, Backbone Coloring for Graphs with Large Girths, Discrete Mathematics, 313 (2013), 1799 -- 1804.
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G. J. Chang, Liu, and X. Zhu, A Short Proof for Chen's Alternative Kneser Coloring Theorem, J. Combinatorial Theory Series A. 120 (2013), 159 -- 163.
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G. J. Chang and Liu, Strong Edge Coloring for Cubic Halin Graphs, Discrete Mathematics, 312 (2012), 1468 -- 1475.
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J. Juan and Liu, Antipodal Labeling for Cycles, Ars Combinatoria, 103 (2012), 81 -- 86.
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S.-J. Kim, Y. Kwon, Liu and X. Zhu, On-line List Colouring of Complete Multipartite Graphs, Electronic J. Combinatorics, 19 (2012), Paper 41, 13 pp.
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K.-W. Lih and Liu, On the Strong Chromatic Index of Cubic Halin Graphs, Applied Math. Letter, 25 (2012), 898 -- 901.
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Liu, Norine, Pan, and X. Zhu, Circular Consecutive Choosibility for k-Choosable Graphs, J. Graph Theory, 67 (2011), 178 -- 197.
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D. Liu, Hamiltonian Spectra for Trees, Ars Combinatoria, 99 (2011), 415 -- 419.
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W. Lin, Liu and X. Zhu, Multi-Colouring the Mycielskian of Graphs, J. Graph Theory, 63 (2010), 311 -- 323.
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J. Juan, Liu and L. Chen, L(j, k)-Labelling for Trees, Disc Applied Math, 158 (2010), 692 -- 698.
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Liu and M. Xie, Radio Number for Square Paths, Ars Combinatoria, 90 (2009), 307--319.
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K.-W. Lih, Liu and W.-F. Wang, On (d,1)-total numbers of graphs, Disc Math, 309 (2009), 3767--3773.
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Liu, Radio Number for Trees, Disc. Math., 308 (2008), 1153--1164.
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Liu, From Rainbow to the Lonely Runner: A Survey, Taiwanese J. Math., 12 (2008), 851--871.
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Liu and X. Zhu, Coloring the Cartesian Sum of Graphs, Disc. Math., 308 (2008), 5928--5936.
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Liu and X. Zhu, Fractional Chromatic Number of Distance Graphs with Two Interval Distance Sets, European J. Combinatorics, 29 (2008), 1733--1743.
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Liu and X. Zhu, The Circular Distance Two Labeling and the L(2, 1)-Number for Outerplanar Graphs, SIAM J. Discrete Mathematics, 19 (2005), 281--293.
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Liu and X. Zhu, Fractional Chromatic Number and Circular Chromatic Number for Distance Graphs with Large Clique Size, J. Graph Theory, 47 (2004), 129--146. Erratum, J. Graph Theory, 48 (2005), 329--330.
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Liu and X. Zhu, Multi-level Distance Labelings and Radio Number for Paths and Cycles, SIAM J. Discrete Mathematics, 19 (2005), 610--621.
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Liu, Circular Chromatic Number of Iterated Mycielski Graphs, Discrete Mathematics, 285 (2004), 335--334.
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Liu and M. Xie, Radio Number for Square of Cycles, Congressus Numerantium, 169 (2004), 105--125.
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Liu and X. Zhu, Circular Distance Two Labelings and Circular Chromatic Numbers, Ars Combinatoria, 69 (2003), 177--183.
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Liu, On sizes of Graphs with Fixed Orders and Spans of Circular Distance Two Labellings, Ars Combinatoria, 67 (2003), 125--139.
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K.-W. Lih and Liu, Circular Chromatic Number of some Reduced Kneser Graphs, J. Graph Theory, 41 (2002), 62--68.
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Liu and X. Zhu, Asymptotic Clique Covering Ratio of Distance Graphs, European J. Combinatorics, 23 (2002), 315--327.
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G. J. Chang, S. Juan and D. Liu, Minimum Span of No-hole (r+1)-Distant Coloring, SIAM J. Discrete Mathematics, 14 (2001), 370--380.
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Liu, Hamiltonicity and Path Covering to Distance Two Labellings of Graphs, Discrete Mathematics, 232 (2001), 163--169.
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G. J. Chang, S. Juan and D. Liu, No-Hole 2-Distant Coloring for Unit Interval Graphs, Ars Combinatoria, 61 (2001), 233--244.
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G. J. Chang, W. Ke, D. Kuo, Liu and R. Yeh, On L(d,1)-Labelings of Graphs, Discrete Mathematics, 220 (2000), 57--66.
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Liu, Chromatic Number of Distance Graphs and the Channel Assignment Problem, Ars Combinatoria, 56 (2000), 65--80.
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K.-W. Lih, Liu and X. Zhu, Star-Extremal Circulant Graphs, SIAM J. Discrete Math, 12 (1999), 491--499.
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G. J. Chang, D. Liu and X. Zhu, Distance Graphs and T-coloring, J. Combin Theory Series B, 75 (1999), 259--269.
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Liu and X. Zhu, Distance Graphs with Missing Multiples in the Distance Sets, J. Graph Theory, 30 (1999), 245--259.
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Liu and R. Yeh, Minimup Span of No-hole T-coloring of Graphs, Congressus Numerantium, 138 (1999), 39--48.
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Liu and R. Yeh, On Distance Two Labellings of Graphs, Ars Combinatoria, 47 (1997), 13--22.
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Liu, T-Graphs and the Channel Assignment Problem, Discrete Math, 161 (1996), 197--205.
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J. Griggs and Liu, Channel Assignment Problem for Mutually Adjacent Sites, J. Combinatorial Theory Series A, 68 (1994), 169--183.
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Liu, On a Conjecture of T-colorings, Congressus Numerantium, 103 (1994), 27--31.
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Liu, T-colorings of Graphs, Discrete Mathematics, 101 (1992), 203--211.
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Liu, Graph homomorphism and the channel assignment problem, Ph.D. Dissertation, University of South Carolina, Columbia, 1991.
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K-W. Lih and Liu, Pascal's Labeling and Path Counting, manuscript.
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Liu, Circular Coloring for Graphs with Distance Constraints, manuscript.
under construction
under construction
EDUCATIONAL BACKGROUND
Ph.D. Math. 1991
- University of South Carolina, Columbia.
- Advisor: Jerrold R. Griggs. Dissertation Title: Graph Homomorphism and the Channel Assignment Problem.
B.S. Math. 1985
- National Central University, Taiwan.