School of Mathematics
Georgia Institute of Technology
Atlanta, Georgia 30332
thomas(at)math.gatech.edu
FAX: 404-894-4409
Mathematical Interests:
Graph theory (including infinite graphs), Combinatorics, Combinatorial
Optimization, Algorithms
Current research:
The
Four Color Theorem and its generalizations,
Hamiltonian graphs on surfaces, embeddings of graphs, topological and structural
graph theory, disjoint paths in graphs, matchings and Pfaffian orientations,
efficient algorithms, perfect graphs.
Research sponsored by
the National Science Foundation.
Recent manuscripts:
- Girth six
cubic graphs have Petersen minors (with N.Robertson and P.D.Seymour).
- Non-planar extensions
of planar graphs (with N.Robertson and P.D.Seymour).
- Packing directed
circuits exactly (with B. Guenin),
arXiv:1012.2749,
to appear in Combinatorica
-
K_6 minors in 6-connected graphs of bounded tree-width
(with K. Kawarabayashi, S. Norin and P. Wollan),
arXiv:1203.2171
-
K_6 minors in large 6-connected graphs
(with K. Kawarabayashi, S. Norin and P. Wollan),
arXiv:1203.2192
-
Three-coloring triangle-free planar graphs in
linear time (with Z. Dvorak and K. Kawarabayashi),
SODA 09 version.
ACM Transactions on Algorithms 7 (2001), article 41,
arXiv:1302.5121.
-
Five-coloring graphs on the Klein bottle
(with N. Chenette, L. Postle, N. Streib, and C. Yerger),
arXiv:1201.5361,
J. Combin. Theory Ser. B. Published online at
http://dx.doi.org/10.1016/j.jctb.2012.05.001.
-
Coloring planar graphs with triangles far apart
(with Z. Dvorak and D. Kral),
arXiv:0911.0885.
-
Nested cycles in large triangulations and crossing-critical graphs
(with C. Hernandez-Velez and G. Salazar),
arXiv:0911.4690.
-
Sub-exponentially many 3-colorings of
triangle-free planar graphs
(with A. Asadi and L. Postle),
arXiv:1007.1430.
-
Deciding first-order properties for sparse graphs
(with Z. Dvorak and D. Kral), to appear in Proceedings of FOCS 2010.
-
Three-coloring triangle-free graphs on surfaces I.
Extending a coloring to a disk with one triangle
(with Z. Dvorak and D. Kral),
arXiv:1010.2472.
-
Three-coloring triangle-free graphs on surfaces II.
4-critical graphs in a disk
(with Z. Dvorak and D. Kral),
arXiv:1302.2158.
-
Testing first-order properties for subclasses
of sparse graphs
(with Z. Dvorak and D. Kral),
arXiv:1109.5036.
-
New Proof of the Weak Structure Theorem
(with K. Kawarabayashi and P. Wollan),
arXiv:1207.6927.
All other papers
Professional Service:
Teaching:
Spring 2013:
Doctoral students:
-
Daniel P. Sanders, Ph.D. 1993. Member of Technical Staff,
Renaissance Technologies
-
Tom Fowler, Ph.D. 1998. Assistant Professor,
Palm Beach Atlantic University.
- Petr Hlineny,
Ph.D. 1999. Associate Professor, Masaryk University, Brno, Czech Republic.
- Barrett Walls, Ph.D. 1999. Associate Professor, Georgia Perimeter College
- Christopher
Carl Heckman, Ph.D. 2000. Lecturer, Arizona State
University
- Jan Thomson, Ph.D. 2000. Instructor, University of Utah.
- Zixia Song, Ph.D. 2004.
Associate Professor, University of Central Florida.
- Paul Wollan,
Ph.D. 2005. Humboldt Fellow, University of Hamburg.
- Sergey Norin,
Ph.D. 2005. Instructor, Princeton University.
- Rajneesh Hegde,
Ph.D. 2006. Software Design Engineer, Microsoft Corporation.
- Torsten Inkmann,
Ph.D. 2008. Member of Technical Staff,
INFORM.
- Carl Yerger,
Ph.D. 2010. Assistant Professor, Davidson College.
- Luke Postle,
Ph.D. 2012. Emory Fellow, Emory University.
- Arash Asadi,
Ph.D. 2012. Member of Technical Staff, Walmart Labs.
- Peter Whalen,
Ph.D. in progress.
- Chun-Hung Liu,
Ph.D. in progress.
Pointers:
