1. Hypergraph matching and Extremal Set Theory

2. Graph theory and combinatorial optimization

3. Graph Factor theory and approximation algorithm

2013.7-Present   Associate Professor, in School of Mathematics and Statistics, Xi’an Jiaotong University

2016.3-2016.5  Visitor, in School of Mathematics, Georgia Tech., Atlanta, USA

2013.11-2014.11  Visitor, in School of Mathematics, Georgia Tech., Atlanta, USA

2010.6-2013.6  Lecturer, in School of Mathematics and Statistics,  Xi’an Jiaotong University

2005.9-2010.6   Ph.D. in Center for Combinatorics, Nankai University, Tianjin, China. Advisor: Prof. Qinglin Yu and Qinghu Hou

2000.9-2004.7   B.S. in Mathematics and Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi Province, China

科研获奖：

1. 中国运筹学会图论与组合分会``青年论文奖"一等奖；

2. 陕西工业与应用数学学会"青年论文奖"二等奖；

3. 西安交通大学青年骨干教师科研考核优秀，破格副教授。

发表论文：

[47] H. Lu and Q. Yu,  An Alternative Proof of General Factor Structure Theorem, submitted.

[46] X. Hou, B. Liu, H. Lu, H-Decomposition of r-graphs when H is an r-graph with exactly k independent edges, submitted.

[45] H. Lu, Yan Wang, Xingxing Yu, Minimum co-degree condition for perfect matchings in k-partite k-graphs, submitted.

[44] H. Lu W. Wang and Y. Jiang, The Complexity of All (g,f)-Factor Problem, preprint.

[43] H. Lu  and M. Kano， Characterization of 1-Tough Graphs using Factors, submitted.

[42] H.  Lu, Guoliang Wang, Surface embedding of non-bipartite k-extendable graphs, submitted.

[41] H. Lu, Qinglin Yu, Binding Number, Toughness and General Matching Extendability in Graphs, submitted.

[40]  H. Lu, Wei Wang, Antifactor of regular bipartite graphs, submitted.

 [39] H. Lu, Yan Wang, Xingxing Yu, On almost perfect matchings in k-partite k-graphs, SIAM. Discrete math., accepted. (SCI)

[38] H. Lu, Xingxing Yu, On Rainbow Matchings for Hypergraphs, SIAM. Discrete math., accepted. (SCI)

[37] H. Lu, Li Zhang, Xingxing Yu, On the number of disjoint perfect matchings in 3-hypergraph, J. Graph Theory, accepted. (SCI)

[36] Haodong Liu, H. Lu, A Degree Condition for a Graph to have (a,b)-Parity Factors, Discrete Math., 341 (2018),  244-252.(SCI)

[35] H. Lu, Guoliang Wang, The maximum number of perfect matchings of semi-regular graphs, Appl. Anal. Discrete Math., 11 (2017),  11–38. (SCI)

[34] H. Lu, Guoliang Wang, A Tutte-type characterization for graph factors, SIAM. Discrete Math., 31 (2017), 1149-1159. (SCI)

[33] H. Lu, Li Zhang, Matching in 3-partite 3-graph, Discrete Math., 340 (2017), 1136-1142. (SCI)

[32]  H. Lu, Yuqing Lin, On The Number of Disjoint Perfect Matchings of Regular Graphs with Given Edge Connectivity,  Discrete Math., 340 (2017), 305–310. . (SCI)

[31] H. Lu, Qinglin Yu, Generalization of Matching Extensions in Graphs (IV): Closures, Graph and Combinatorics, Vol 32, (2016), 2009-2018. (SCI)

[30] H. Lu, Vertex-Coloring Edge-Weighting of Bipartite Graphs with Two Edge Weights, Discrete Mathematics & Theoretical  Computer Science, Vol 17, No 3 (2016). (SCI)

[29] H. Lu, An Extension of Cui-Kano's Characterization Problem on Graph Factors, J. Graph Theory, 81 (2016), 5-15. (SCI)

[28] H. Lu, Yuqing Lin, Maximum spectral radius of graphs with given connectivity, minimum degree and independence  number, J. Discrete Algorithms,   31 (2015),113–119.

[27] H. Lu, Wei, Wang, Yuqing, Lin, On edge connectivity and parity factor, Acta Math. Sin. (Engl. Ser.) 31 (2015), 772-776.

[26] H. Lu and Guoliang Wang,  Surface embedding of (n,k)-extendable graphs. Discrete Appl. Math. 179 (2014), 163–173.(SCI)

[25] Xiao Huan, H. Lu and Qinglin Yu, Threshold for matching-covered graphs, Gongcheng Shuxue Xuebao, 31 (2014), 163-173.

[24]  S. Liu, H. Zhang, H. Lu and Y. Lin, A note on the strong edge-coloring of outerplanar graphs with maximun degree 3, Acta Math. Appl. Sin. Engl. Ser., 32 (2016),  883–890. (SCI).

[23]  H. Lu and W. Wang, On Perfect k-Matchings, Graphs and Combin., 30 (2014), 229-235. (SCI)

[22]  H. Lu, G. Wang and Q. Yu, On the Existence of General Factors in Regular Graphs, SIAM J.    Discrete Math., 27 (2013), 335-343. (SCI)

[21] X. Liu, H. Lu, W.Wang and W. Wu, PTAS for the minimum k-path connected vertex cover problem in unit disk graphs,  J. Global Optim., DOI: 10.1007/s10898-011-9831-x. (SCI)

[20]  H. Lu and Guoliang Wang, On Cui-Kano's Characterization Problem on Graph Factors, J. Graph Theory, DOI: 10.1002/jgt.21712. (SCI)

[19]  H. Lu, Simplified existence theorems on all fractional [a,b]-factors, Discrete Appl. Math., 161 (2013), 2075-2078. (SCI).

[18]  H. Lu and Y. Lin,  Maximum spectral radius of graphs

 with  connectivity at most  k and minimum degree at least $delta$, Lecture Notes in Computer Science, accepted.

[17]  H. Lu and Y. Lin, Note on Parity Factors of Regular Graphs, Electronic Journal of Graph Theory and Applications, 1(1) (2013), 50–55.

[16]  W. Wang, L. Mao and H. Lu, On biregular graphs determined by their generalized characteristic polynomials, Linear Algebra Appl.,438 (2013), 3076-3084. (SCI)

[15]  H. Lu et.al, On Super-connectivity of (4,g)-Cages, Graphs and Combin., 29 (2013), 105-119. (SCI)

[14]  H. Lu,  Regular graphs, eigenvalues and regular factors, J.  Graph Theory,  69 (2012), 349-355. (SCI)

[13]  Y. Duan, H. Lu and Q. Yu, L-factors and adjacent-distinguish edge-weighting, East Asian Journal on Applied mathematics, 2 (2012), 83-93. (SCIE)

[12]  H. Lu,  Wei Wang, and Bing Bai, Vertex-deleted subgraphs and regular factors from regular graph, Discrete Math., 311 (2011), 2044-2048. (SCI)

[11]  H. Lu, Y. Wu, Q. Yu and Y. Lin, New improvements on the connectivity of cages, Acta Mathematica Sinica, 6 (2011), 1163-1172. (SCI)

[10]  W. Wang, F. Li, H. Lu and  Z. Xu, Graphs determined by their generalized characteristic polynomials, Linear Algebra Appl., 434 (2011), 1378-1387. (SCI)

[9]   B. Bai, H. Lu and Q. Yu, Generalization of matching extensions in graphs (III)., Discrete Appl. Math., 159 (2011), 727-732. (SCI)

[8]   H. Lu,  and Qinglin Yu, General Fractional f-Factor Numbers of Graphs, Appl. Math. Lett., 24 (2011), 519-523. (SCI)

[7]  H. Lu, Q. Yu and C. Zhang, Vertex-coloring 2-edge-weighting of graphs, European J. Combin.,  32 (2011), 22-27. (SCI)

[6]  H. Lu and Q. Yu, Constructive proof of deficiency  theorem of  (g, f)-factor, Sci.China Math., 53 (2010), 1657-1662.  (SCI)

[5]  H. Lu, Z. Wu and X. Yang, Eigenvalues and  [1, n]- odd factors, Linear Algebra Appl., 433 (2010), 750-757. (SCI)

[4]  H. Lu, Regular factors of regular graphs from eigenvalues,  Electron. J. Combin., 17 (2010), R159. (SCI)

[3]  M. Kano, H. Lu, and Q. Yu, Component factors with large components in graphs, Appl. Math. Lett., 23 (2010), 385-389. (SCI)

[2]   Y. Lin, H. Lu, Y. Wu and Q. Yu, On super connectivity of (4,g)-cages with even girth, Networks, 56 (2010), 143-148. (SCI)

[1]   H. Lu, X. Yang and Q. Yu, On vertex-coloring edge-weighting of graphs, Front. Math. China, 4 (2009), 325-334. (SCI)

电子邮箱：luhongliang@mail.xjtu.edu.cn

联系电话：029-82665578