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Professor Guizhen Liu
          Professor Guizhen Liu was born in 1944, received the B.S. degree in 1968 and the M.S. degree in 1981 from the Department of Mathematics, Shandong University , respectively. She began her academic career at Shandong University since 1981 and became a full professor in 1992. She visited Simon Fraser University of Canada as an assistant professor from 1985 to 1987. And visited the Chinese University of HongKong, the University of HongKong, HongKong Baptist University, City University of HongKong as a visiting scholar respectively since 1996. She has published over 130 journal papers and 4 books and has been a reviewer for Mathematics Review. She received 7 Science and Technical Awards from Shandong Province and 5 times from Chinese National Education Council. She has been listed in the Marquis Who's Who in the World.
     Research Interests
  • Graph theory
  • Matroid theory
  • Combinatoric Optimization
     Books
  • Liu G.,and Chen Q., Matroid Theory, National Univ of Defence Tech Press, 1994.
  • Xie L.,Liu J.,and Liu G., Graph and Combinatorial Topology, Shandong University Press, 1994.
  • Diao Z.,Zheng H.,Liu J.,and Liu G., Operational Research, Higher Education Press, 1996. ( Textbook Series for 21st Century )
  • Li B.,and Liu G., Skills and Method of Advanced Algebra, Shandong Science & Techology Press, 1999.
     Representative Publications since 1990
  1. Liu Guizhen, Deng Xiaotie, A polynomial algorithm for finding (g,f)-coloring orthogonal to stars in bipartite graphs, Science in China Ser A Mathematics (2005) 48(3), 233-332. (SCI)
  2. Liu Guizhen, Zhang Lanju, Properties of fractional k-factors of graphs, Acta. Math. Scientia 25 B (2) (2005), 301-304. (SCI)
  3. Song Huimin, Liu Guizhen, On f-edge cover-coloring of simple graphs, Acta. Math. Scientia 25 B (1) (2005), 145-151. (SCI)
  4. Liu Guizhen, Liu Yan, On (g,f)-uniform graphs, Acta Math. Appl. Sinica, English Ser. 21(4) (2005), 57-76.
  5. Liu Guizhen, W. Zang, f-factors in bipartite (m,f)-graphs, Discrete Applied Math. 136(1) (2004). (SCI)
  6. Yan Liu, Guizhen Liu, Number of maximum matchings of bipartite graphs with positive surplus, Discrete Math. 274 (2004), 311-318. (SCI)
  7. Ma Yinghong, Liu Guizhen, Some results on fractional k-extendable graphs, Chinese Journal of Engineering Mathematics 21(4)(2004), 567-573. (EI)
  8. Yan Jin, Liu Guizhen, Vertex-disjoint quadrilaterals in bipartite graphs, J. Systems Science and complexing17(4) (2004), 532-537.
  9. Bian qiuju, Liu Guizhen, (g,f)-factors with special properties in bipartite (mg,mf)-graphs, Appl. Math. J. Chinese Univ. Ser B 19(2) (2004)133-139.
  10. Diao Kefeng, Liu Guizhen, Upper bounds on minimum number of C-edgesod 4-uniform C-hypergraphs, Mathematica Applicata 17 (4) (2004), 623-628.
  11. Liu Guizhen, Feng Haodi, Yu Jiguo, 2-factors with some properties in 2d-regular graphs, Proceedings of the international conference on Mathematical programming, Shanghai University press (2004),251-258. (ISTP)
  12. Yan Jin, Liu Guizhen, A new result on independent large cycles in bipartite graphs, Proceedings of the international conference on Mathematical programming, Shanghai University press (2004), 400-404. (ISTP)
  13. Song Huimin, Liu Guizhen, Aplications of an equitable edge-coloring theorems, Proceedings of the international conference on Mathematical programming, Shanghai University press (2004), 350-355. (ISTP)
  14. Feng Li, Liu Guizhen, Edge disjoint graphs in (mg+k-1,mf-k+1)-graphs, Proceedings of the international conference on Mathematical programming, Shanghai University presof the international conference on Mathematical programming, Shanghai University press (2004), 163-169. (ISTP)
  15. Guizhen Liu, Binhai Zhu, Some problems on factorizations with constrains in bipartite graphs, Discrete Applied Math. 128 (2003), 421-434. (SCI)
  16. Yu Jiguo, Liu Guizhen, (g,f)-factors in bipartite (mg,mf)-graphs, Mathematica Applicata 16(1) (2003), 126-129.
  17. Guizhen Liu et al., A PTAS for minimizing total completion time of bounded batch scheduling, LNCS 2337(2002), 304-314. (SCI, ISTP)
  18. H. Feng and Guizhen Liu, Orthogonal factorizations of graphs, J. Graph Theory 40(4) (2002), 267-278. (SCI)
  19. Y. Liu, Guizhen Liu, The fractional matching numbers of graphs, Networks 40(3) (2002), 228-231. (SCI)
  20. Liu Guizhen, Long Heping, Randomly orthogonal (g,f)-factorizations in graphs, Acta. Appl, Math. Sinica, English Ser. (2002). 18(3), 489-494.
  21. Miao Lianying, Liu Guizhen, Edge covered coloring and fractional edge covered coloring, J. of Systems . Science. and complexing (2002).15(2), 187-193.
  22. Wu Jianliang and Liu guizhen, The linear arboricity of composition graphs, J. Sys. Sci. and Com. (2002). 15(4), 372-375.
  23. Guizhen Liu and Q. Yu, Generalization of matching extensions in graphs, Discrete Math. 213 (2001), 231,311-320. (SCI)
  24. Liu Guizhen, Zhang Lanju, Fractional (g,f)-factors of graphs, Acta. Math. Scientia 21B(4) (2001), 541-545. (SCI)
  25. Liu Guizhen, Dong Henian, Orthogonal (g,f)-factorizations of bipartite graphs, Acta Math. Scientia 21B(3) (2001), 316-322. (SCI)
  26. G. Li, Guizhen Liu, A generalization of orthogonal Factorizations in graphs, Acta Mathematica Sinica, English Series 17(4) (2001), 669-678. (SCI)
  27. Yan Xiaoxia, Liu Guizhen, Edge disjoint (g,f)-factors orthogonal to r disjoint subgraphs in (mg+k,mf-k)-graphs, Mathematica Applicata, 2001,14(4) 37-41.
  28. P. C. B. Lam, Guizhen Liu et al., Orthogonal (g,f)-factorizations in networks, Networks 35(4) (2000), 285-287. (SCI)
  29. Liu Guizhen, On (g, f)-uniform graphs, Advance in Mathematics 29(3), (2000)£¬285-287.
  30. Liu Guizhen and Zhang Lanju, Maximum fractional (0, f)-factors of graphs, Mathematica Applicata,(2000),13(1),31-35.
  31. Guizhen Liu, Q. Yu, k-factors and extendability with prescribed components, congr. Numer. (1999)£¬139£¬77-88 (ISTP).
  32. L.Miao, G.Liu, An extension of one theoremn of critical edge-chromatic graphs, Mathematica Applicata,1999,12(3), 69-71.
  33. Guizhen Liu, Q. Yu, Toughness and perfect matchings in graphs, Ars combinatoria, (1998), 41(3), 267-272. (SCI)
  34. G. Li and Guizhen Liu, (g,f)-factorizations orthogonal to a subgraph in graphs, Science in China SerA, (1998), 41(3), 267-272. (SCI)
  35. L. Xie, Guizhen Liu, B. Xu, On endo-homology of complexs of graphs, Discrete Math., (1998), 188, 285-291. (SCI)
  36. Guizhen Liu, Q. Yu, On n-edge-deletable and n-critical graphs, Bulletin of the ICA, (1998), 24, 65-72.
  37. Liu Guizhen and Wang Jianfang, (a,b,k)-critical graphs, Advanced in Mathematics,(1998),27(6),536-540.
  38. G.liu and J.Wang, (a,b,k)-critical graphs, Chinese Science Bulletin, (1997), 42(17), 1492-1493. (SCI)
  39. Li Guojun and Liu Guizhen,(g,f)-factorizations Orthogonal to a subgraph in graphs, Science in China A 40(1997).
  40. Li Guojun and Liu Guizhen, Factorization orthogonal to a subgraph in graphs, Advanced in Mathematics,(1997),26(5),464-468.
  41. Liu Guizhen, A 2-factorization orthogonal to a star in a graph, J.Sys.Sci and Math.Scis.9:1(1996)38-42.
  42. G. Liu and G. Yan, Orthogonal [k-1,k+1]-factorizations in graphs, J. Statistical and inference 51(1996)195-200.(SCI)
  43. Liu Guizhen, (g,f)-factorizations orthogonal to a star in graphs, Science in China A38:7(1995)805-812.(SCI)
  44. Xie Litong and Liu Guizhen,Combinatorics Graph Theory Algorithms and Applications,World Scientific Publishing Co.(1995)389-397.
  45. G. Liu and Q. Yu, Star-factors of vertex-deletion graphs, Congr.Number.107(1995)155-160.
  46. Xie Litong and Liu Guizhen,On Whitney's and Tutte's conjecture,Acta Math. Sinica 38:3(1995)289-293.
  47. G.Liu, Orthogonal (g,f)-factorizations in graphs.discrete math.143(1995)153-158.(SCI)
  48. Liu Guizhen, Some conditions for f-covered graphs, Acta Math.Scientia 14(1994)91-97.
  49. Liu Guizhen, (g,f)-factors and factorizations in graphs, Acta Math. Sinica 37:2(1994)230-237.
  50. Liu Guizhen, On solutions of Alspach problems, Chinese Science Bulletin 39:7(1994)541-544.(SCI)
  51. Liu Guizhen, the Paths between two vertices in tree graphs, J. Sys. Sci and Math. Scis. 5:2(1992)108-110.
  52. G. Liu, B. Alspach and K. Heinrich, Some results on orthogonal factorizations in graphs, Advance of Mathematics 21:2(1992)211-215.
  53. S. Chen and G. Liu, Toughness of graphs and [a,b]-factors with prescribed properties, JCMCC 12(1992)215-221.
  54. Liu Guizhen, Toughness and k-covered graphs, J. Appl. Sciences 15:3(1992)391-402.
  55. B.Alspach, K.Heinrich and G.liu ,Orthogonal factorizations of graphs, Contemporary Design Theory:A collection of surveys, John Wiley and sons Inc(1992)13-37.
  56. K. Heinrich, P. Hell and G. Liu, A simple existence criterion for (g,f)-factors, Discrete Math, 85(1990)313-317.(SCI)
  57. Liu Guizhen, Proof of a conjecture on matroid base graphs, Science in China A 33: 11(1990)1329-1337.(SCI)
     Representative Publications Before 1990
  1. B.Alspach and G.Liu, Paths and cycles in Matroid base graphs, graph and Combinatorics 5:3(1989)207-211.(SCI)
  2. G. Liu, On [a,b]-covered graphs, JCMCC 5(1989)14-22.
  3. Liu Guizhen, Regular k-covered graphs, Acta Math, Scientia9:2(1989)39-43.(SCI)
  4. G. Liu, A lower bound on connectivities of matroid base graphs, Discrete Math,69:1(1988)55-60.
  5. G. Liu, On connectivities of tree graphs, J.Graph Theory,(1988)12(3),453-459.(SCI)
  6. Zheng H. and Liu Guizhen, some properties on Paths in matroid base graphs, J. Sys. Sci. and Math. Sci. 1:2(1988)104-108.
  7. K. Heinrich and G. Liu, A lower bound 0n the number of spanning trees with k end vertices, J. Graph Theory 12:1(1988)95-100.
  8. G. Liu, On connectivities of base graph of some matroids, J. Sys. Sci. and Math Scis 1:1(1988)18-21.
  9. G. Liu, On f-covered graphs, Congr. Number. 61-(1988),81-86.
  10. Liu Guizhen, On (g,f)-covered graphs, Acta Math.Scientia,8:2(1988)181-184.(SCI)
  11. Liu Guizhen, The connectivities of adjacent tree graphs, Acta Math, Appl.Sinica,3:4(1987)313-317.
  12. Liu Guizhen, A theorem on the 1-factors of r-hypertrees, Advance of Mathematics, 15:4(1986)381-383.
  13. Liu Guizhen, On the lower bound of Chartrand's problem in simple graphs, J. Appl. Sciences4:4(1986)322-325.
  14. Liu Guizhen, Welsh's conjecture is true for simple binary matroids, Kexue Tong bao 30:9(1985)1147-1150.
  15. Liu Guizhen, An algorithm for lexicographically generating ordered rooted trees, J. sys. Sci. and math.Scis.5(1985)15-19.
  16. Liu Guizhen, A theorem on the 1-factors of (m,n)-trees, Acta Math.Scientia 5:3(1985)267-170.
  17. Liu Guizhen, Matroid complexes-geometrical representations on Matroids, Acta Math, Scientia5:1(1985)35-42.
  18. Liu Guizhen, A lower bound in solutions of chartrands problem, Acta Math. Appl. Sinica 1:1(1984)93-96.
     Post-graduates Supervision
    She became a post-graduate supervisor from 1989. From then on, she has directed 22 post-graduates, 17 of which have been   awarded Master degree. From 1992, she began to direct PHD students. She has supervised 16 PHD students, 10 of which have been   awarded PHD degree.
     Main Curriculums
  • Undergraduate Courses: The Complementarity of Advanced Algebra; Graph Theory; Linear Programming; Discrete Mathematics;                                                Western Economics; Combinatorial Mathematics.
  • Post-graduate Courses: Matroid Theory; Combinatorial Topology and Graph Theory; Graph Factors Theory; Graph Coloring                                                Problems; Operational Research.
To Contact Prof. Liu