**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,
*36 (2014) 7-16.

* 29. *Xu, R.,* *On the Second
Neighborhood Conjecture, *Journal of Combinatorial Mathematics and *

* Combinatorial
Computing, *88 (2014) 143-146..

* 28. *Xu, R., Strong 5-cycle double covers of graphs*,
Graphs and Combinatorics, *30(2) (2014)

495-499.

* 27*. Luo, R., Miao Z. and Xu, R., Nowhere-Zero
3-flows of graphs with independent number 2,

* Graphs and Combinatorics*, 29(6)
(2013) 1899-1907.

* * 26. Xu, R.., Two equivalent properties of
Z3-connectivity, *Graphs and Combinatorics*, 29(6)
(2013)

1983-1987.

* *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 Z`_{3}-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 S*ciences 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:**

32. “On Integer Flows of Graphs” 1-hour talk for REU students, University of West

Georgia, Carrollton,
GA July 18, 2014

31. “Cycle double covers and long circuits of graphs”,
invited talk, the 1097^{th} AMS Meeting

Special Session on Graph Theory, University of
Tennessee , Knoxville, TN, March 21^{st} –

March 23^{rd},
2014.

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 1087^{th}

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

March
1^{st} –March 3^{rd}, 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 Z_{3}-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 Z_{3}-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.