Hong-Jian Lai


Department of Mathematics
West Virginia University
Morgantown, WV 26506-6310
Phone: (304)-293-2011 EXT 2348 (OFFICE)
E-MAIL: hjlai@math.wvu.edu

 

EDUCATION

·        Ph.D. in Mathematics, Wayen State University, Detroit, Michigan (1988).

·        MS in Mathematics, Wayen State University, Detroit, Michigan (1985).

·        BS in Mathematics, S. China Institute of Technology, Guangzhou, P. R. CHINA (1982).

 

HONORS AND AWARDS:

  • West Virginia University Foundation Outstanding Teaching Award, West Virginia University (2005-2006).
  • Eberly College of Arts and Sciences Outstanding Teaching Award, West Virginia University (2005-2006).
  • Eberly College of Arts and Sciences Outstanding Research Award, West Virginia University (1995-1996).
  • Post Doctoral Fellowship in University of Waterloo (1988 - 1989).
  • Rumble Fellowship in Wayne State University (1984 - 1985, 1987-1988).
  • The Bharucha-Reid Award for outstanding achievement in the Ph.D. program, Wayne State University (1988).
  • The Hidegoro Nakano Award for outstanding achievement in the Masters program, Wayne State University (1985).

 

PROFESSIONAL EXPERIENCE:

  • Professor, West Virginia University (2000-present).
  • Associate Professor, West Virginia University (1995-1999).
  • Assistant Professor, West Virginia University (1989-1995).
  • Post Doctoral Fellow and Adjunct Lecturer, University of Waterloo (1988-1989).

 

PhD STUDENTS SUPERVISED

  • Ju Zhou (graduation year: 2008)
    Position: Assistant Professor,     Bridgewater State College    , Bridgewater, MA.
  • Yehong Shao (graduation year: 2005)
    Position: Assistant Professor, Ohio University Southern, Ironton, OH.
  • Mingquan Zhan (graduation year: 2003)
    Position: Assistant Professor, Millersville University, Millersville, PA.
  • Xiangwen Li (graduation year: 2002)
    Position: Post Doctoral Fellow, University of Regina, Canada.
  • Bruce Montgomery (graduation year: 2001)  (Industry)
  • Kamal Hennayake (graduation year: 1998)
    Position: Assistant Professor, Mountain State University, Beckly, WV.
  • Xiankun Zhang (graduation year: 1998)
    Position: Software Engineer, IMCI Technologies, Arlinton, VA.

PhD STUDENTS CURRENTLY UNDER MY SUPERVISION

  • Huiya Yan (Expected graduation year: 2009)
  • Liang Yanting (Expected graduation year: 2010)
  • Li, Hao (Expected graduation year: 2010)

MASTER STUDENTS SUPERVISED

  • Jong-Suk Hwang (graduation year: 1994)
  • Robert Pierce (graduation year: 1995)
  • Xiaodong Shi (graduation year: 1997)
  • Nathan Sams (graduation year: 1998)
  • Jessica Soloweigh (graduation year: 1999)
  • Hoifung Poon (graduation year: 2000)
  • Jingjing Chen (graduation year: 2003)
  • Mia Chung (graduation year: 2004)
  • Hehui Wu (graduation year: 2005)
  • Mellisa Kay (graduation year: 2008)
  • Senmei Yao (graduation year: 2008)
  • Zuhe Zhang (graduation year: 2008)

RESEARCH GRANTS:

Year

Title of Grant

Amount

1991-1993

ONR grant N00012-91-J-1699

$52,012

1993

Senate Research Grant of WVU

$5,000

1995

WV Epscor Grant

$3,000

1994-1996

NSA grant MDA904-94-H-2012

$26,006

2003-2006

ONR DEPSCoR N00014-03-1-0660

$43,160

2003-2006

DOE EPSCoR DE-FG02-00ER45829

$15,146

2005

College Mini-Grant (research on math model of aging process)

$5,000

2006-2007

Extension of ONR DEPSCoR N00014-03-1-0660

$20,318

2006-2008

DOE (Department of Energy) DE-FC26-06NT42793

$18,233

 

 

 

 

PUBLICATION (Books):

  1. Matrices in Combinatorics and Graph Theory, (with Bolian Liu), Kluwer Academic Publishers, Vol. 3 of Network Theory and Applications, (2000), (ISBN: 0-7923-6469-4).
  2. Matroid Theory (in Chinese), Chinese Higher Education Press, (2002), (ISBN: 7-04-010563-2)

Applications of Mathematics:

  1. Energy Management System with Automatic Reconfiguration for Electric Shipboard Power Systems, (with Shilpa B. Ganesh, Karl Schoder, Amer Al-Hinai, Ali Feliachi), Proceedings, Reconfiguration and Survivability Symposium 2005, Atlantic Beach, FL. Feb 16-18, 2005.
  2. Distributed Control Agents Approach to Energy Management In Electric Shipboard Power Systems, (with Ali Feliachi, Karl Schoder and Shilpa B. Ganesh), IEEE PES General Meeting, June 18-22, 2006, Montral, Canada.
  3. Distributed Approaches for Determinations of Reconfiguration Algorithm Termination, (with Ali Feliachi, Karl Schoder and Pinak Jayant Tulpule), submitted.
  4. Age distribution and risk factors for the onset of severe disability among community-dwelling older adults with functional limitations, (with Y. Wu, H. Huang, B Wu, and S. McCrone), The Journal od Applied Gerontology, accepted.

 

PUBLICATIONS (Research Papers):

  1. Unique graph homomorphisms onto odd cycles, Utilitas Mathematica 31(1987), 199-208. (88e:05041).
  2. On the hamiltonian index, Disc. Math. 69 (1988) 43-53. (89f:05113).
  3. Contractions and hamiltonian line graphs, J. Graph Theory 12 (1988) 11-15. (89f:05114).
  4. Unique graph homomorphisms onto odd cycles, II, J. of Combinatorial Theory, Series B, 46 (1989) 363-376. (90c:05088).
  5. Reduced graphs of diameter two, J. Graph Theory, 14 (1990) 77- 87. (91b:05157).
  6. The size of strength-maximal graphs, J. Graph Theory, 14 (1990) 187-197. (91f:05075).
  7. Eulerian subgraphs in graphs with short cycles, (with Paul A. Catlin) Ars Combinatoria, 30 (1990), 177-191. (91j:05070).
  8. Eulerian subgraphs in a class of graphs, Ars Combinatoria, 31 (1991) 302 - 311. (92d:05095).
  9. Cycle covers in graphs without subdivisions of K_4, (with H. Y. Lai) J. of Comb. Math and Comb. Computing, 9 (1991), 201-207. (92d:05126).
  10. A note on uniformly dense matroids, (with H. Y. Lai) Utilitas Mathematica, 40 (1991) 251-256. (92h:05029).
  11. Cycle covering of plane triangulations, (with H. Y. Lai) J. of Comb. Math. and Comb. Computing, 10 (1991) 3-21. (92i:05160).
  12. Graphs whose edges are in small cycles, Disc. Math., 94 (1991) 11-22. (92j:05111).
  13. Small cycle covers of planar graphs, (with H. Y. Lai) Congressus Numerantium, 85 (1991) 203-209. (93c:05046).
  14. Spanning trails joining two given edges, (with Paul A. Catlin) in ``Graph Theory, Combinatorics, and Applications'' (vol. 1), eds by Y. Alavi, G. Chartrand, O. Oellermann and A. Schwenk, Kalamazoo, (1991), 207-222. (93e:05052).
  15. Graphs of diameter at most two, Ars Combinatoria, (1992) 331-343. (93m:05100)
  16. Nowhere-zero 3-flows of highly connected graphs, (with C. Q. Zhang) Discrete Math, 110 (1992) 179-183. (93m:05105).
  17. Uniformly dense generalized prisms over graphs, (with Hobbs, H. Y. Lai and G. Weng) Congressus Numerantium 91 (1992) 99-105. (93m:05164).
  18. Duality of graph families, (with H. Y. Lai) Discrete Math. 110 (1992) 165-177. (93m:05195).
  19. Supereulerian complementary graphs, J. Graph Theory, 17 (1993) 263-273. (94a:05137).
  20. Fractional arboricity, strength and principal partitions in graphs and matroids, (with P. A. Catlin, J. W. Grossman, A. M. Hobbs) Discrete Appl. Math. 40 (1992) 285-302. (94g:05070).
  21. Graph without K_4-minors, (with H. Y. Lai) Ars Combinatoria, 36 (1993) 327-334. (94i:05078).
  22. Edge-maximal (k,l)-graphs, (with C. Q. Zhang) J. Graph Theory, 18 (1994) 227 - 240. (95g:05065).
  23. Collapsible graphs and Matchings, (with Z. H. Chen) J. Graph Theory, 17 (1993) 597-605. (95a:05082).
  24. Nowhere-zero flows in some regular graphs, (with Z. H. Chen, H.Y. Lai, G. Weng) Congressus Numerantium, 97 (1993) 205-208. (95b:05085).
  25. Small circuit double covers of cubic multigraphs, (with X. X. Yu and C. Q. Zhang) J. Combin. Theory (B), 60 (1994) 177 - 194. (95b:05122).
  26. Jackson's conjecture on eulerian subgraphs, (with Z. H. Chen, H. Y. Lai, G. Weng), Combinatorics, Graph Theory, Algorithms and Applications, (eds. by Y. Alavi et al), 53-58, World Scientific, River Edge, NJ (1994). (95k:05111).
  27. Hamiltonian connected line graphs, (with C. Q. Zhang) Ars Combinatoria, 38 (1994) 193 - 202. (96b:05099).
  28. Cycles in line graphs, (with Z. H. Chen) Congressus Numerantium, 105 (1994) 129 - 133, (97a:05130).
  29. Every 4-connected line graph of a planar graph is hamiltonian, Graphs and Combinatorics, 10 (1994) 249 - 253. (95i:05084).
  30. Large survivable nets and the generalized prisms, Discrete Appl. Math., 61 (1995) 181-185. (96e:05141).
  31. The size of graphs with given inclusive connectivity, Ars Combinatoria, 41 (1995) 225-239. (96e:05142).
  32. Strength and fractional arboricity of complementary graphs, (with G. Weng) Discrete Math., 143 (1995) 141-151. (96f:05104).
  33. Vertex arboricity and maximum degree, (with P. A. Catlin) Discrete Math., 141 (1995) 37-46. (96i:05045).
  34. The size of graphs without nowhere-zero 4-flows, J. Graph Theory, 19 (1995) 385-395. (96k:05119).
  35. Supereulerian graphs and excluded induced minors, Discrete Math., 146 (1995) 133-143. (96k:05124).
  36. Every matroid is a submatroid of a uniformly dense matroid, Discrete Appl. Math., 63 (1995) 151-160. (97a:05050).
  37. Reduction techniques for super-Eulerian graphs and related topics—a survey, (with Z. H. Chen), Combinatorics and graph theory 95, Vol. 1 (Hefei), 53-69, World Sci. Publishing, River Edge, NJ, 1995. (98h:05126).
  38. A note on the strong 2-cover conjecture for graphs without K_5-minors, (with H. Y. Lai), J. Combin. Math. and Combin. Computing, 20 (1996) 242-244. (96m:05153).
  39. Supereulerian graphs and the Petersen graph, (with Catlin), J. Combinatorial Theory, Ser B, 66 (1996) 123-139. (97a:05144).
  40. A property on Edge-disjoint spanning trees (with H.Y. Lai and Payan), Europ. J. Combinatorics, 17 (1996) 447-450. (97d:05064).
  41. Reduction towards collapsibility, Graph Theory, Combinatorics, and Algorithms, eds. Y. Alavi and A. Schwenk, John Wiley and Sons, New York, (1995), 661-670 . (97f:05187).
  42. A note on mod (2p+1)-orientatable graphs, J. Combin. Math. Combin. Computing, 22 (1996) 223-224. (97i:05053).  
  43. Graphs without spanning eulerian subgraphs, (with P. A. Catlin and Z. Han), Discrete Math., 160 (1996) 81-91. (97m:05166).
  44. Cycle covers of planar graphs, Congressus Numerantium, 122 (1996) 33-46. (97k:05126).
  45. The higher-order edge touchness of a graph and truncated uniformly dense matroids, (with Z. H. Chen), J. Combin. Math. Combin. Computing, 22 (1996) 157-160. (97i:05063).
  46. Generalized matroid packing and covering, (with Z.-H. Chen and Y. Kuang) Congressus Numerantium, 127 (1997) 155-160. (98j:05045).
  47. Eulerian subgraphs containing given vertices and hamiltonian line graphs, Discrete Math., 178 (1998) 93-107. (99d:05094).
  48. Supereulerian graph and the Petersen graph, II, (with Z.-H. Chen), Ars Combinatoria, 48 (1998) 271-282. (99c:05123).
  49. Group coloring and group connectivity of graphs, (with Chen, Lei and Zhang), Congressus Numerantium, 134 (1998), 123-130. (99j:05068).
  50. The strength and the l-edge-conenctivity, (with K. Hennayake and X. Lei), Bull. of ICA, 26 (1999), 58-70. (99m:05092).
  51. Even subgraphs of a graph, (with Z. H. Chen), Combinatorics, graph theory, and algorithms, Vol. I, II (Kalamazoo, MI, 1996), 221--226, New Issues Press, Kalamazoo, MI, 1999. MR1985055.
  52. Extending a partial nowhere zero 4-flow, J. Graph Theory, 30 (1999), 277-288. (2000c:05077).
  53. Edge integrity maximal graphs, (with X. K. Zhang), J. Combin. Math. Combin. Comput. 30 (1999) 237-250. (2000d:05063).
  54. Connectivity in cycle matroid and bicircular matroids, (with Chen and Kuang), Ars Combinatoria, 52 (1999), 239-290. (2001d:05032).
  55. Graph homomorphisms into the odd cycle, (with B. Liu), Bulletin of the Inst. of Combin. and Appl., 28 (2000), 19-24. (2000i:05106).
  56. Group connectivity of 3-edge-connectied chordal graphs, Graphs and Combinatorics, 16 (2000), 165-176. (2001f:05074).
  57. Spanning trails connecting two given edges, (with X. K. Zhang) Ars Combinatoria, 57 (2000), 301-318. (2001h:05059).
  58. Eulerian subgraph containing given edges, Discrete Math, 230 (2001), 61-69. (2001k:05135).
  59. Nowhere zero flows in line graphs, (with Chen and H. Y. Lai), Discrete Mathematics, 230 (2001), 133-141. (2001k:05193).
  60. Extremal size of graphs without a nowhere zero 3 flow, (with Lei Xu) Bulletin of the Inst. of Combin. and Appl., 32 (2001), 90-95. ((2002a:05146).
  61. Graph families operations, (with Catlin and Hobbs), Discrete Math, 230 (2001), 71-97. (2002b:05124).
  62. Line graphs and forbidden induced subgraphs (with Soltes) J. Combinatorial Theory, Ser. B, 82 (2001) 38-55. (2002d:05104).
  63. Hamilton weights and Petersen minors, (with C. Q. Zhang), J. Graph Theory, 38 (2001),  197-219. (2002g:05120).
  64. Group colorability of graphs,  (with X. Zhang), Ars Combinatoria, 62 (2002), 299-317. MR1881968 (2003c:05109)
  65. Group chromatic number of graphs without K_5-minors, (with X. Zhang) Graphs and Combinatorics, 18 (2002), 147--154. (2002m:05089).
  66. Cycle cover ratio of regular matroids, (with H. Poon), Europ. J. Combinatorics, 23 (2002), 1007-1014.  MR1938354 (2003h:05062) 
  67. Nowhere zero 3-flows in locally connected graphs,  J. Graph Theory, 42 (2003), no. 3, 211--219. MR1958145 (2003m:05110)
  68. Eulerian subgraph in 3-edge-connected graphs and hamiltonian line graphs, (with Zhihong Chen, Xiangwen Li, Deying Li and Jingzhong Mao) J. Graph Theory, 42 (2003), no. 4, 308--319. MR1963103 (2004a:05090)
  69. Small cycle cover of 2-connected cubic graphs, (with X. Li), Discrete Math., 269 (2003), no. 1-3, 295--302. MR1989470 (2004d:05159)
  70. Upper bound of dynamic chromatic number, (with B. Montgomery and H. Poon), Ars Combinatoria, 68 (2003), 193--201.  MR1991048 (2004e:05077)
  71. Minimally (k,k)-edge-connected graphs, (with K. Hennayake, Deying Li and Jingzhong Mao), J. Graph Theory, 44 (2003), no. 2, 116—131
  72. Global asymptotic stability in a rational recursive sequence, (with Yang, Xiaofan; Evans, David J.; Megson, Graham M.) Appl. Math. Comput. 158 (2004), no. 3, 703--716.
  73. Generalized honeycomb torus is Hamiltonian, (with Yang, Xiaofan; Evans, David J.; Megson, Graham M.) Inform. Process. Lett. 92 (2004), no. 1, 31--37.
  74. On the maximal connected component of hypercube with faulty vertices, (with Xiaofan Yang, David J. Evans, Bill Chen, Graham M. Megson), Int. J. Comput. Math. 81(5): 515-525 (2004).
  75. Eulerian subgraphs and hamiltonian connected line graphs, (with Li and Zhan), Discrete Applied Math 145 (2005) 422-428.
  76. Hamiltonian N_2-locally Connected Claw-Free Graphs, (with Shao and Zhan), J. Graph Theory, 48 (2005), 142--146. 05C40 (05C45)
  77. Supereulerian planar graphs, (with Deying Li, Jingzhong Mao and Mingquan Zhan), Ars Combinatoria, 75 (2005) 313-331. 
  78. Nowhere zero 4-flow in regular matroids, (with X. Li and H. Poon), J. Graph Theory, 49 (2005) 196-204. 
  79. Spanning trails connecting given edges, (with Li, Ou and Poon), Graphs and Combinatorics, 21 (2005) 77-88. 
  80. Group Chromatic number of graph, (with X. Li), Graphs and Combinatorics, 21 (2005) 469-474.
  81. Group connectivity of graphs with diameter at most 2, (with X. J. Yao), European J. Combin., 27 (2006) 436-447.
  82. Group Chromatic number of planar graphs with girth at east 4, (with X. Li), J. Graph Theory, 52 (2006) 51-72. 
  83. Hamiltonicity in 3-connected Claw-Free Graphs, (with Yehong Shao and Mingquan Zhan), J. of Combinatorial Theory, Series B. 96 (2006) 571-576.
  84. Every 3-connected, essentially 11-connected claw-free graph is hamiltonian, (with Y. Shao, H. Wu, and J. Zhou), J. of Combinatorial Theory, Series B. 96 (2006) 493-504.
  85. Conditional Colorings of Graphs, (with S. Fan, J. Lin, B. Montgomery, and Z. Tao), Discrete Math, 306 (2006) 1997-2004.
  86. Collapsible biclaw-free graphs, (with X. J. Yao), Discrete Math, 306 (2006) 2115-2117.
  87. Erratum: Collapsible Biclaw-free Graphs, (with X. J. Yao), Discrete Math, 307 (2007) 1217.
  88. Spanning eulerian subgraphs in claw-free graphs, (with Chen, Luo and Shao),  J. Combinatorial Theory and Combinatorial Computing 59 (2006), 165--171. 05C45  
  89. New sufficient condition for hamiltonian graphs, (with Y. Shao and K. Zhao), Applied Math Letters, 20 (2007), no. 1, 116-122.
  90. Quadrangularly connected claw-free graphs, (with M. Li, C. Guo, L. Xiong, D. Li), Discrete Math. 307 (2007) 1205-1211.
  91. Problems related to hamiltonian line graphs, (with Yehong Shao), AMS/IP Studies in Advanced Mathematics, 39 (2007), 149-159.
  92. On circular flows of graphs, (with R. Xu and C. Q. Zhang), Combinatorica, 27 (2007) 245-246.
  93. An inequality for the group chromatic number of a graph, (with X. Li and G. Yu), Discrete Math., 307 (2007) 3076-3080.
  94. Mod $(2p+1)$-orientations and $K_{1, 2p+1}$-decompositions, SIAM J. of Discrete Math., 21 (2007) 844-850.
  95. An $s$-Hamiltonian Line Graph Problem，(with Z. H. Chen, D. Y. Li and W. Shiu), Graphs ad Combinatoircs, 23 (2007), 241-248.
  96. Spanning cycles in regular matroids without $M^*(K_5)$ minors, (with B. Liu, Y. Liu and Y. Shao), European J. Combinatorics, 29 (2008), no. 1, 298-310.
  97. Edge-connectivity and edge-disjoint spanning trees, (with Catlin and Y. Shao), Discrete Math., accepted.
  98. Group connectivity of certain graphs, (with J. Chen, E. Eschen), Ars Combinatoria, accepted.
  99. Reinforcing the number of disjoint spanning trees, (with Z. H. Chen), Ars Combinatoria, accepted.
  100. Regular matroids without disjoint circuits, (with S. Fan, Y. Shao, H. Wu and J. Zhou), Ars Combinatoria, accepted.
  101. Spanning eulerian subgraphs in $N^2$-locally connected claw-free graphs, (with Li, Shao and Xiong), Ars Combinatoria, accepted.
  102. New Sufficient Conditions for s-Hamiltonian Graphs and s-Hamiltonian Connected Graphs, (with J. Yan, K. Zhao, and J. Zhou), Ars Combinatoria, accepted.
  103. Degree Sequence and Supereulerian Graphs, (with Y. Shao, T. Zhang and J. Zhou), Discrete Math., accepted.
  104. Hamilton-Connected Indices of Graphs, (with L. Xiong and H. Yan), Discrete Math., accepted.
  105. On s-hamiltonian-connected line graphs, (with Liang and Shao), Discrete Math., accepted.
  106. The $s$-Hamiltonian Index, (with Eschen, Shao, and Zhang), Discrete Math., accepted.
  107. Every 4-connected line graph of a quasi claw-free graph is hamiltonian connected, (with Shao, and Zhan), Discrete Math., accepted.
  108. Hamiltonian graphs involving neighborhood conditions, (with L. Zhang, Y. and K. Zhao), Ars Combinatoria, accepted.  
  109. On group connectivity of graphs, (with R. Xu and J. Zhou), Graphs and Combinatorics, accepted.
  110. Hamiltonian connectedness in 3-connected line graphs， (with Yehong Shao, Gexin Yu and Mingquan Zhan), Discrete Applied Math. Accepted.
  111. Every line graph of a 4-edge-connected graph is ${\bf Z}_3$-connected, (with Lianying Miao and Yehong Shao),  European J. Combinatorics, accepted.
  112. On mod $(2p+1)$-orientations of graphs, (with Y. H. Shao, H. Wu and J. Zhou), J. of Combinatorial Theory, Series B., accepted.
  113. Nowhere zero 3-flows in triangularly connected graphs, (with G. Fan, R. Xu, C. Q. Zhang, and Q. Zhou), J. of Combinatorial Theory, Series B., accepted.
  114. Obtaining a uniformly dense graph from a non-uniformly dense graph, (with Hobbs, H. Y. Lai  and Layana), Discrete Applied Math, accepted.