Songling Shan | Curriculum VitaeDepartment of Mathematics, Vanderbilt University

1326 Stevenson Center, Nashville, TN 37240H (678)200-8090 • T (615)343-6276

B songling.shan@vanderbilt.eduÍ https://my.vanderbilt.edu/shans1/homepage/

AppointmentNon-tenure-track Assistant Professor (Postdoc) Aug. 2015–Department of Mathematics, Vanderbilt University

Information Technology Assistant Aug. 2010–Aug. 2012Department of Mathematics and StatisticsGeorgia State UniversityData Modeling Analyst June 2014–Aug. 2014AT&T contractor through Experis, Manpower Group

EducationPh.D., Mathematics,Georgia State University May 2015Advisor: Dr. Guantao ChenM.S., Statistics,Georgia State University Aug. 2014Advisor: Dr. Gengsheng QinM.S., Mathematics,East China Normal University July 2011Advisor: Dr. Han RenB.S., Mathematics,Northwest Normal University, China July 2008

Academic Awards{ Outstanding Graduate Student Award Georgia State University 2015

{ Brains and Behavior Fellowship Georgia State University 2012–2014

{ Ph.D. Dissertation Grant Award Georgia State University 2013

{ V. V. Lavroff Scholarship Georgia State University 2013

{ Outstanding Graduate Scholarship (grade 1) East China Normal University 2008–2010

{ Provincial Second Prize in Northwest Normal University 2006

China Undergraduate Mathematical Contest in Modeling{ Outstanding Student Scholarship (grade 1) Northwest Normal University 2005–2007

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Research InterestsGraph Theory and Combinatorics. Topics include structural graph theory, graph colorings,and extremal graph theory.

PapersPublished or Accepted:

16. Chromatic index determined by fractional chromatic index (with Guantao Chen, YupingGao, Ringi Kim, and Luke Postle), J. Combin. Theory Ser. B, to appear, 2018.

15. Antimagic orientation of biregular bipartite graphs (with Xiaowei Yu), ElectronicJ.Combinator., 24 (4): #P4.31, 2017.

14. Forbidden pairs and the existence of a spanning Halin subgraph (with Guantao Chen,Jie Han, Suil O, and Shoichi Tsuchiya), Graphs Combin., 33 (2017), no. 5, 1321-1345.

13. Spanning trails with maximum degree at most 4 in 2K2-free graphs (with GuantaoChen, Mark Ellingham, and Akira Saito), Graphs Combin., 33 (2017), no. 5, 1095-1101.

12. Vizing’s 2-factor conjecture involving large maximum degree (with Guantao Chen), J.Graph Theory, 86 (2017), no. 4, 422-438.

11. Nonempty intersection of longest paths in series-parallel graphs (with Guantao Chen,Julia Ehrenmüller, Cristina G. Fernandes, Carl Georg Heise, Ping Yang, and Amy Yates),Discrete Math., 340 (2017), no. 3, 287-304.

10. Equitable vertex arboricity of 5-degenerate graphs (with Guantao Chen, Yuping Gao,Guanghui Wang, and Jianliang Wu), J. Combin. Opt., 34 (2017), no. 2, 426-432.

9. Characterizing forbidden pairs for hamiltonian squares (with Guantao Chen), GraphsCombin., 31 (2015), no. 6, 2113-2124.

8. Disjoint chorded cycles of the same length (with Guantao Chen, Ronald J. Gould,Kazuhide Hirohata, and Katsuhiro Ota), SIAM J. Discrete Math., 29 (2015), no. 2,1030-1041.

7. The existence of a 2-factor in a graph satisfying the local Chvátal-Erdős condition (withGuantao Chen and Akira Saito), SIAM J. Discrete Math., 27 (2013), no. 4, 1788-1799.

6. Homeomorphically irreducible spanning trees (with Guantao Chen), J. Combin. TheorySer. B, 103 (2013), no. 4, 409-414.

5. On equitable vertex distinguishing edge colorings of trees (with Bing Yao and XiangenChen), Acta Math. Sci. Ser. B Engl. Ed., 33 (2013), no. 3, 621-630.

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4. Homeomorphically irreducible spanning trees in locally connected graphs (with GuantaoChen and Han Ren), Combin. Probab. Comput., 21 (2012), no. 1-2, 107-111.

3. Genus of Cm,n and strong genus embedding of Km,n (with Han Ren), J. East ChinaNorm. Univ. Natur. Sci. Ed., 2011, no. 2, 17-21.

2. Inverse eigenvalue problem for nonnegative matrices, J. East China Norm. Univ. Natur.Sci. Ed., 2009, no. 4, 35-37.

1. The k-balancings of two families of graphs, Journal of Gansu Normal Colleges, Vol.12(2007), no. 5, 13-15.

Submitted:

7. Vizing’s 2-factor conjecture involving maximum degree and toughness conditions (withJinko Kanno). Available as arXiv:1709.02241.

6. Hamiltonian cycles in 3-tough 2K2-free graphs. Available as arXiv:1706.09029.

5. Toughness and spanning trees in K4-minor-free graphs (with Mark Ellingham, DongYe, and Xiaoya Zha). Available as arXiv:1704.00246.

4. Nonempty intersection of longest paths in 2K2-free graphs (with Gili Golan). Availableas arXiv:1611.05967.

3. Dirac’s Condition for Spanning Halin Subgraphs (with Guantao Chen). Available asarXiv:1505.06181.

2. Difference of forbidden pairs containing a claw (with Guantao Chen, Michitaka Furuya,Shoichi Tsuchiya, and Ping Yang). Available as arXiv:1505.00386.

1. Regular colorings and factors of regular graphs (with Anton Bernshteyn, Omid Khormali,Ryan R. Martin, Jonathan Rollin, Danny Rorabaugh, and Andrew J. Uzzell). Availableas arXiv:1603.09384.

In Preparation:1. New bounds for locally irregular chromatic index of graphs (with Mark Ellingham, Ryan

Solava, and Xiaowei Yu)2. Toughness for bounded treewidth (with Mark Ellingham, Dong Ye, and Xiaoya Zha).3. Spanning k-trees and k-trails from degree sum conditions (with Mark Ellingham and

Yi Zhang).4. Minimum degree condition for spanning generalized Halin graphs (with Guantao Chen

and Ping Yang).

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5. A lower bound on circumferences of 3-connected graphs with bounded maximum degrees(with Guantao Chen, Zhicheng Gao, and Xingxing Yu).

Grants{ PI of NSF Research Grant: Graph Toughness and Edge Colorings Decision pending

{ Co-PI of NSF Conference Grant (DMS-1707486) 2017

Twenty-Ninth Cumberland Conference on Combinatorics, Graph Theory and Computing

Teaching ExperienceVanderbilt University:

Current Course:{ Math 3320/5320: Error-correcting Codes and CryptographyCourses Taught:{ Math 1200: Single-Variable Calculus I Fall 2016{ Math 2410: Methods of Linear Algebra Spring 2016/2017{ Math 3320/5320: Error-correcting Codes and Cryptography Spring, Fall 2017{ Math 4710/6710: Graph Theory Fall 2016/2017Teaching Assistant:{ Math 1300: Accelerated Single Variable Calculus (two sections) Fall 2015

Georgia State University:Courses Taught:{ Math 1101: Intro to Mathematical Modeling Fall 2012/2013Course Developer/Teaching Assistant:{ Math 1101: Intro to Mathematical Modeling Fall 2014, Spring 2015

East China Normal University:Teaching Assistant:{ Ordinary Differential Equations Fall 2008{ Advanced Algebra I Spring 2010

PresentationsInvited Conference Talks:{ Circumferences of 3-connected graphs with bounded maximum degrees

Jan. 2018AMS Special Session on Connections in Discrete Mathematics: Graphs, Hypergraphs, and Designs.

2018 Joint Mathematics Meetings. San Diego, CA.

{ Vizing’s 2-factor conjecture involving toughness and maximum degree conditionsSep. 2017

AMS Special Session on Graph Connectivity and Edge Coloring. University of Central Florida.

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{ Spanning cycles, walks, and trails in 2K2-free graphs Mar. 2017AMS Special Session on Graph Theory. College of Charleston.

{ Toughness condition for k-trees in K4-minor-free graphs Jan. 2017AMS Special Session on Topics in Graph Theory. 2017 Joint Mathematics Meetings. Atlanta, GA.

{ Vizing’s 2-factor conjecture involving large maximum degree Mar. 2016AMS Special Session on Topics in Graph Theory. University of Georgia.

{ Spanning k-trees and k-trails from degree sum conditions Nov. 2015Atlanta Lecture Series in Combinatorics and Graph Theory XVI. Georgia Institute of Technology.

{ Vizing’s 2-factor conjecture involving large maximum degree Sep. 2014AMS Special Session on Graph and Hypergraph Theory. University of Wisconsin-Eau Claire.

{ Generalized spanning Halin subgraphs in graphs with larger minimum degrees Jan.2014Atlanta Lecture Series in Combinatorics and Graph Theory XI. Georgia State University.

{ Homeomorphically irreducible spanning trees Feb. 2013Atlanta Lecture Series in Combinatorics and Graph Theory VIII. Georgia State University.

Contributed Conference Talks:{ Dirac’s condition for spanning Halin subgraphs Aug. 2015

International Conference on Graph Theory and Applications. Middle Tennessee State University.

{ Vizing’s 2-factor conjecture involving large maximum degree May 201427th Cumberland Conference on Combinatorics, Graph Theory & Computing. West Virginia University.

{ Generalized spanning Halin subgraphs in graphs with larger minimum degrees Apr.201410th Graduate Student Combinatorics Conference. Auburn University.

{ Disjoint chorded cycles of the same length May 201326th Cumberland Conference on Combinatorics, Graph Theory & Computing. Middle Tennessee State

University.

Colloquium & Seminar Talks:{ Spanning cycles, walks, and trails in 2K2-free graphs Oct. 2016

Discrete Mathematics Seminar, Middle Tennessee State University.

{ Homeomorphically irreducible spanning trees and Halin graphs Jan. 2015Colloquium, Department of Mathematical Sciences, Georgia Southern University.

{ Homeomorphically irreducible spanning trees and Halin graphs Jan. 2015Discrete Mathematics Seminar, Kennesaw State University.

{ Graph Theory and Combinatorics Seminar, Vanderbilt University (5 times) 2015–2017{ Discrete Mathematics Seminar, Georgia State University (6 times) 2011–2015Poster Presentations:{ Homeomorphically irreducible spanning trees May 2012

Conference on Graph Theory. Georgia Institute of Technology.

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{ Homeomorphically irreducible spanning trees May 2012Paul Erdős Memorial Lecture Series. The University of Memphis.

Professional ActivitiesReviewer for Mathematical Reviews: Reviewer since 2014Referee for Journals: Journals include Advances and Applications in Discrete Mathemat-ics, Ars Combinatoria, Canadian Journal of Chemistry, Discrete Mathematics, Graphs andCombinatorics, Journal of Combinatorics, Journal of Global Optimization, SIAM Journalon Discrete Mathematics, Theory and Applications of Graphs, and The AustralasianJournal of CombinatoricsConference & Seminar Organizations:{ Organizer of (upcoming) AMS Special Session on Selected Topics in Graph Theory

April 2018Vanderbilt University, Nashville, TN.

{ Organizer of Vanderbilt Graph Theory and Combinatorics Seminar Spring 2017Vanderbilt University, Nashville, TN.

{ Co-organizer of 29th Cumberland Conference on Combinatorics, Graph Theory andComputing May 2017Vanderbilt University, Nashville, TN.

{ Co-organizer of AMS Special Session on Topics in Graph Theory Jan. 2017Joint Mathematics Meetings, Atlanta, GA.

{ Co-organizer of Special Session on Topics in Graph Theory AMS Spring SoutheasternSectional Meeting Mar. 2016University of Georgia, Athens, GA.

Other:{ Participant of Rocky Mountain-Great Plains Graduate Research Workshop in Combina-

torics Jun. 1–12, 2015Iowa State University, Ames, IA.

Computer Skills & Certification{ Skills: Experienced with SageMath, Matlab, R, and SAS{ Certification: SAS Certified Base Programmer for SAS 9 credential

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ReferencesDr. Guantao ChenDept. of Mathematics & Statistics, GSU25 Park Place, Room 1317Atlanta, GA 30303Office phone: (404)-413-6436Email: gchen@gsu.edu

Dr. Mark EllinghamDept. of Mathematics, Vanderbilt UniversitySC 1514, 1326 Stevenson CenterNashville, TN 37240Office phone: (615)-322-6670Email: mark.ellingham@vanderbilt.edu

Dr. Frank Hall (concerns teaching)Dept of Mathematics & Statistics, GSU25 Park Place, Room 1317Atlanta, GA 30303Office phone: (404)-413-6432Email: fhall@gsu.edu

Dr. John Ratcliffe (concerns teaching)Dept. of Mathematics, Vanderbilt UniversitySC 1326D, 1326 Stevenson CenterNashville, TN 37240Office phone: (615)-322-6665Email: j.g.ratcliffe@vanderbilt.edu

Dr. Akira SaitoDept. of Computer Science and System Analysis, Nihon UniversitySakurajosui 3-25-40, Setagaya-Ku, Tokyo 156-8550, JAPANEmail: asaito@chs.nihon-u.ac.jp

Dr. Xiaoya ZhaDept. of Mathematical Sciences, MTSUKOM 271, MTSU Box 34Murfreesboro, TN, 37132Office phone: (615) 898-2494Email: xiaoya.Zha@mtsu.edu

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