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:

 
8. “Note on Z3-connectivity of graphs”, in preparation. 
7. “Realizing degree sequences with A-connected graphs”, in preparation.
6. “Graph decomposition problems”, in preparation. 
5. “Degree sum and Z3-connectivity”, completed.
4. “On Potentially W­­4- graphic Sequences”, completed.
3. “On 2-factors in bipartite graphs”, completed.
2. “Group connectivity of graphs satisfying Ore-condition”, submitted

      1. “Z4-connected graphs satisfying degree sum condition”, submitted.

 

Publications:

 

      21. 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, accepted, 2008.
20. 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.
19. Xu, R., Note on cycle double covers of graphs, Discrete Mathematics, accepted, 2007
18. Luo, R., Xu, R., Yin, J.-H. and Yu, G-X., Ore-condition and Z3-connectivity, 
      European Journal of Combinatorics, accepted, 2007
17. Lai, H.-J., Xu, R. and Zhou, J., On group connectivity of graphs,  
     Graphs and Combinatorics, accepted, 2007
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:

     

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”, paper present at  

              Twentith 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”, paper 
             present at 2007 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”, paper present at  

              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,” paper present at 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,” paper present at 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,” paper presented at Advances in Graph and

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

7.       Xu, R., “On circular flows of graphs,”  paper presented at 37th Midwest Graph Theory 

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

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

                  paper presented at   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,”

      paper presented at 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,” paper presented at 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,” paper

      presented at 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,”

      paper presented at 8th Chinese Conference on Graph Theory,

      Taiyuan, China, April 1994.

Professional Memberships:

Mathematical Association of America (MAA)