Hong-Jian Lai

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 Determination of Reconfiguration Algorithm Termination, (with Pinak Tulpule, Karl Schoder, Ali Feliachi),  Proceedings of the Electric Ship Technologies Symposium (ESTS) 2007, Arlington, VA, May 21-23, 2007.
  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 of Applied Gerontology, 26 (2007) 258-273.
  5. Health Behavior and Transition of Physical Disability Among Community Dwelling Older Edults, (Part1, 2, 3, 4)  (with Y. Wu and S. McCrone), Research on Aging, 30 (2008) 572-591.

 

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, (Part A, Part B) (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, (Part 1, Part 2) 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. On group connectivity of graphs, (with R. Xu and J. Zhou), Graphs and Combinatorics, 24 (2008) 1-9.
  98. Hamiltonian connected hourglass free line graphs, (with D. X.  Li, Y, H, Shao and M. Q. Zhan), Discrete Math., 308 (2008) 2634-2636.
  99. Hamiltonian connected graphs, (with K. W. Zhan and Ju Zhou), Computers and Mathematics with Applications, 55 (2008) 2707-2714.
  100. New Sufficient Conditions for s-Hamiltonian Graphs and s-Hamiltonian Connected Graphs, (Part 1, Part 2, Part 3) (with J. Yan, K. Zhao, and J. Zhou), Ars Combinatoria, 88 (2008), 217-227.
  101. Group connectivity of certain graphs, (with J. Chen, E. Eschen), Ars Combinatoria, 89 (2008).
  102. On s-hamiltonian-connected line graphs, (with Liang and Shao), Discrete Math., 308 (2008) 4293-4297.
  103. Every 4-connected line graph of a quasi claw-free graph is Hamiltonian connected, (with Shao, and Zhan), Discrete Math., 308 (2008) 5312-5316.
  104. 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., 98 (2008) 1325-1336.
  105. Edge-connectivity and edge-disjoint spanning trees, (with Catlin and Y. Shao), Discrete Math., accepted.
  106. Reinforcing the number of disjoint spanning trees, (with Z. H. Chen), Ars Combinatoria, accepted.
  107. Regular matroids without disjoint circuits, (with Suohai Fan, Yehong Shao, Hehui Wu and Ju Zhou), Ars Combinatoria, accepted.
  108. Spanning eulerian subgraphs in $N^2$-locally connected claw-free graphs, (with Li, Shao and Xiong), Ars Combinatoria, accepted.
  109. Degree Sequence and Supereulerian Graphs, (with Yehong Shao, Taoye Zhang and Ju Zhou), Discrete Math., accepted.
  110. Hamilton-Connected Indices of Graphs, (with Liming Xiong and Huiya Yan), Discrete Math., accepted.
  111. The $s$-Hamiltonian Index, (with Elaine Eschen, Yehong Shao, and Lili Zhang), Discrete Math., accepted.
  112. Hamiltonian graphs involving neighborhood conditions, (with Lili Zhang, Yehong  Shao and Kewen Zhao), Ars Combinatoria, accepted.  
  113. Hamiltonian connectedness in 3-connected line graphs， (with Yehong Shao, Gexin Yu and Mingquan Zhan), Discrete Applied Math. Accepted.
  114. Every line graph of a 4-edge-connected graph is ${\bf Z}_3$-connected, (with Lianying Miao and Yehong Shao),  European J. Combinatorics, accepted.
  115. On mod $(2p+1)$-orientations of graphs, (with Y. H. Shao, H. Wu and J. Zhou), J. of Combinatorial Theory, Series B., accepted.
  116. Transforming a graph into a uniformly dense graph, (with A. M. Hobbs and L. Hannan), Discrete Applied Math, accepted.
  117. Multi-$g$ base index of primitive anti-symmetric sign pattern matrices (with Yanting Liang and Bolian Liu) Linear and Multilinear Algebra, accepted.

 

 

 

 

 

.