Research Interests:

Research interests are graph and combinatorics, discrete optimization, operations research and mathematical programming, especially in the areas of integer flows and cycle double covers of graphs, graph factors, and graph coloring problems.

Recent papers:

        4.  “Path Cover Number in 4-regular Graphs”, in preparation.

           3.  “Graph decomposition problems”, in preparation.

        2.  “Extendibility of contractible configurations for flows of graphs”, completed.

  1.  “Cycle double covers and long circuits of graphs”, submitted.
 

Publications:

    

        30. Luo, R., Miao Z.  Xu, R and Zhang, C.-Q., Nowhere-zero 3-flows of graphs with prescribed sizes of odd edge cuts, European Journal of  Combinatorics, accepted 2013

 

       29. Xu, R., On the Second Neighborhood Conjecture, Journal of Combinatorial Mathematics and Combinatorial Computing (conference proceedings), accepted 2012.

 

      28. Xu, R., Strong 5-cycle double covers of graphs, Graphs and Combinatorics, DOI: 10.1007/s00373-012-1266-8 Online First, 2012     

 

      27. Luo, R., Miao Z. and Xu, R., Nowhere-Zero 3-flows of graphs with independent number 2, Graphs and Combinatorics, DOI: 10.1007/s00373-012-1238-z,Online First, 2012    

 

      26. Xu, R.., Two equivalent properties of Z3-connectivity, Graphs and Combinatorics, DOI: 10.1007/s00373-012-1197-4 Online First, 2012.

 

      25. Luo, R., Xu, R., and Yu, G., An extremal  problem on group connectivity of graphs,  European  Journal of  Combinatorics, 33 (6) (2012) 1078-1085.

     

24. Zhang, X, Zhan M., Xu, R., Shao, Y.,  Li, X.,  and Lai, H.-J., Degree sum condition for Z3-connectivity in graphs, Discrete Mathematics , 310  (2010) 3390-3397.

 

23. Xu, R., Note on cycle double covers of graphs, Discrete Mathematics, 309 (2009) 1041-1042.
 
      22. Fan, G., Lai, H.-J., Xu, R., Zhang, C.-Q. and Zhou, C.,  Nowhere-zero 3-flows in triangularly connected graphs, Journal of Combinatorial Theory,  
             Ser. B, 98 (2008) 1325-1336.
 
21. Luo, R., Xu, R., Zang, W.-A. and Zhang, C.-Q., Realizing degree sequences with graphs having nowhere-zero 3-flows, SIAM Journal on Discrete Mathematics, 22 (2) (2008),  500–519.
 
20. Luo, R., Xu, R., Yin, J.-H. and Yu, G-X., Ore-condition and Z3-connectivity, European Journal of Combinatorics, 29(7)(2008), 1587-1595
 
19. Lai, H.-J., Xu, R. and Zhou, J., On group connectivity of graphs, Graphs and Combinatorics, 24(2008), 195-203, 2008
 
18. Sun, Z. J., Xu, R. and Yin, J-H., Group connectivity of graphs satisfying Ore-condition, Proceeding of the 2008 International Conference on Foundations of Computer Science (ISBN:1-60132-066-3) CSREA Press (2008) 21-24.
 
17. Liu, G.Z., Qian, J.B, Sun, J. Z. and Xu, R., Bipartite toughness and $k$-factors in bipartite graphs, International Journal of Mathematics and Mathematical Sciences, (2008)  Art. ID 597408, 8 pp.
 
16. Lai, H.-J., Xu, R. and Zhang C.-Q., Note on circular flow numbers of graphs,  Combinatorica, 27 (2007) 245-246.
 
15. Khodkar, A. and Xu, R. “More on even [a,b]-factors in graphs”,  Discussiones Mathematicae Graph Theory, 27 (1) (2007) 193-204.
 
14. DeVos, M., Xu, R. and Yu, G., Nowhere-zero Z3-flows through Z3-conncetivity, Discrete mathematics 306 (2006) 26-30.
 
13. Xu, R. and Zhang, C.-Q, On flows in bidirected graphs, Discrete Mathematics 299(2005) 335-343.
 
12. Xu, R., Note on acyclic colorings of graphs, Ars Combinatoria 72 (2004), 235-339.
 
11. Xu, R. and Yu, Q. L., Some conditions for graphs to be k-extendable, Congressus  Numerantium 163 (2003), 189-195. 
 
10. Xu, R. and Yu, Q. L., An Ore-type condition for the existence of k-factors with  prescribed properties, Congressus Numerantium 162 (2003), 97-109.
 
9.  Xu, R. and  Zhang, C.-Q., Nowhere-zero 3-flows in squares of graphs,  Electronic Journal of Combinatorics 10 (2003): R5.
 
8. Xu, R. and Yu, Q. L., Note on toughness and (k, r)-factor-critical graphs,  Bulletin of the Institute of Combinatorics and its Applications 29 (2000): 85-87.
 
7. Xu, R., Some Ore-type conditions for the existence of connected [2, k]-factors in graphs, Discrete Mathematics 194 (1999), no. 1-3: 295-298.
 
6. Xu, R., Connected [1, k]-factors of balance bipartite graphs. Systems Science and Mathematical Sciences 12 (1999), no. 2: 149-153.
 
5. Xu, R. and Yu, Q. L., (4, k)-factor-critical graphs and toughness,  Advances in Mathematics (China) 28 (1999), no. 6: 539-540.
 
4. Xu, R., A sufficient condition for graphs to have 2-connected [2, 4]-factors,  Advances in Mathematics (China) 26 (1997), no. 4: 379-380.
 
3. Xu, R., The connectivity of adjacent tree graphs. Shandong Daxue Xuebao Ziran Kexue Ban 32 (1997), no. 4: 412-419. 
 
2. Xu, R., [a, b]-factors in K­­­­­1,­n-free graphs,  Shandong Daxue Xuebao Ziran Kexue Ban 31 (1996), no. 2: 173-177. 
 
1. Xu, R., A lower bound on the connectivities of adjacent tree graphs. Pure and Applied Mathematics 10 (1994), Special Issue: 168-173.
 

Academic Presentations:

 

     30. “On Integer flow and group connectivity of graphs”, 1-hour invited talk on the COSM

           Dean’s Research Seminar, University of West Georgia, April 5, 2013

 

     29.  “On modular-(2k+1) contractibility and extension consistency”   invited talk, the 1087th

           AMS Meeting Special Session on Graph Theory, University of Mississippi, Oxford, MS,

           March 1st –March 3rd, 2013

    

     28. “Nowhere-zero 3-flows of graphs with independence number 2”, contributed talk,

           the 25th Annual    Cumberland Conference on Graph Theory, Combinatorics, and

           Computing, East Tennessee State University, Johnson City, TN, May 10-12, 2012.

 

     27. “Nowhere-zero 3-flows of graphs with prescribed size of odd edge cuts”, contributed talk,

           the 24th Annual    Cumberland Conference on Graph Theory, Combinatorics, and

           Computing, University of Louisville, Louisville, KY, May 12-14, 2011.

 

     26. “On group connectivity and average degree of graphs”, contributed talk, the 23rd

          Annual    Cumberland Conference on Graph Theory, Combinatorics, and Computing,

          The University of Mississippi, Oxford, MS, May 20-22, 2010

 

25.  “On group connectivity of graphs”, invited 1-hour seminar talk, School of Mathematics,

          Georgia Institute of Technology, Atlanta, GA Feb. 26, 2010

 

24. “On flows of graphs”, 1-hour talk for REU students, University of West Georgia,

        Carrollton, GA June 29, 2009

 

23. “On group connectivity of graphs” , invited 1-hour colloquium talk, Middle

       Tennessee State University, Murfreesboro, TN March 16, 2009

 

22.  “On 3-path decompositions of planar bipartite graphs”, contributed talk,  the 22nd

          Annual    Cumberland Conference on Graph Theory, Combinatorics, and Computing,

          Western   Kentucky University, Bowling Green, KY, TN May 21-23, 2009

 

 

21.   Xu, R. “Group connectivity of graphs satisfying Ore-condition”, contributed talk, The

       2008 International Conference on Foundations of Computer Science, Las Vegas, NV

       July 14-17, 2008.

 

20.   Xu, R. “Realizing degree sequences with graphs having nowhere-zero 3-flows”, invited

        1-hour seminar talk, University of Southern Mississippi, Hattiesburg, MS May 30, 2008

 

19.    Xu, R. “Degree sum condition and Z­3-connectivity”, contributed talk, 21st Annual

              Cumberland Conference on Graph Theory, Combinatorics, and Computing, Vanderbilt  

              University, Nashville, TN May 15-17, 2008.

 

     18.   Xu, R. “Ore-condition and Z­3-connectivity”, contributed talk, MIGHTY XLXI,

       West Virginia University, Morgantown, WV April 26, 2008

 

17.    Xu, R. “Degree Sequences and nowhere-zero 3-flows of graphs”, primary presenter. 
        1-hour seminar talk at Georgia State University, Atlanta, GA September 11, 2007.
 

16.     Xu, R. “All generalized Tutte-orientations and Z3­-connectivity”, contributed talk,

20th Annual Cumberland Conference on Graph Theory, Combinatorics, and 

              Computing, Emory University, Atlanta, GA May 17-19, 2007.

 

     15.   Xu, R. “Realizing degree sequences with graphs having nowhere-zero 3-flows”,   
             contributed talk,AMS Sectional Meeting, University of Arizona, April 21-22, 2007
 

     14.   Xu, R. “Realizing degree sequences with graphs having 3-flows” primary 

       presenter. 1-hour seminar talk at UWG, August 28, 2006

 

     13.   Xu, R., “Graphic Sequences and Nowhere-Zero 3-Flows of Graphs”, contributed talk,    

              Nineteenth Annual Cumberland Conference on Graph Theory, Combinatorics, and

              Computing, East Tennessee State University May 18-20, 2006

 

     12.  Xu, R.., “On integer flows of bidirected graphs,” contributed talk, MIGHTY XLI,

       Middle Tennessee State University, Sep. 24, 2005

 

     11.  Xu, R. “Nowhere-zero Z-3-flows through Z-3-connectivity” primary presenter. 1-hour

             seminar talk at UWG, Nov. 28, 2005

 

     10.   Xu, R., “On integer flows of bidirected graphs,” contributed talk, CombinaTexas 2005,

       Texas State University-San Marcos, February 25-26, 2005

 

9.   Xu, R., “On integer of bidirected graphs,” primary presenter. 1-hour seminar talk at  

      UWG, Nov. 6, 2004

 

8.   Xu, R., “On circular flows of graphs,” contributed talk, Advances in Graph and

      Matroid Theory, Ohio State University, December 13-16, 2003

 

7.      Xu, R., “On circular flows of graphs,”  contributed talk, 37th Midwest Graph Theory 

      Conference, Valparaiso University, Valparaiso, IN, September 20th, 2003.

 

       6.   Xu, R., “Group connectivity of triangulated connected graphs,”

                  contributed talk, 15th   Cumberland Conference on Combinatorics, Graph Theory,

                 and Computing, Georgia State University, Atlanta, GA, May 17th, 2003.

             

5.      Xu, R., “Group connectivity of squares of graphs,” contributed talk, 35th Midwest Graph

      Theory Conference, Illinois State University, Normal, IL, September 28th, 2002

 

4.   NSF-CBMS Regional Research Conference: Structure and Decomposition of Graphs.

      East Tennessee State University, Johnson City, TN, May 20th-May 24th 2002,

      conference attended.

 

3.    Xu, R., “An Ore-type condition for the existence of k-factors with prescribed         

properties,” contributed talk, 10th Chinese Conference on Graph Theory,

      Yantai, China, August 1999.

 

2.      Xu, R., “An Ore-type condition for graphs to have 2-connected [2, 4]-factors,” contributed

      talk,  the Summer School and International Conference on Combinatorics”97,

Hefei, China, June 1997.

 

1.    Xu, R., “A lower bound on connectivities of adjacent tree graphs,”

      contributed talk, 8th Chinese Conference on Graph Theory,

      Taiyuan, China, April 1994.