Research

Craig Larson, Professor, Department of Mathematics, VCU


Math with Jack, photo by Kathie Cameron
Photo by Kathie Cameron.


Refereed Papers

32. P. Brooks, D. Edwards, C.E. Larson, and N. Van Cleemput, Conjecturing-Based Computational Discovery of Patterns in Data, arXiv preprint, submitted.

31. A. Bradford, J. K. Day, L. Hutchinson, B. Kaperick, C. E. Larson, M. Mills, D. Muncy, and N. Van Cleemput, Automated Conjecturing II: Chomp and Reasoned Game Play, Journal of Artificial Intelligence Research (JAIR), 68 (2020) 447--461.

30. C. E. Larson, (Avoiding) Proof by Contradiction: the Square-root-of-2 is Not Rational, arXiv preprint.

29. R. Jacobs, C.E. Larson, A Graph-Theoretic Formula for the Number of Primes, in Integers: Electronic Journal of Combinatorial Number Theory, Vol. 20A (2020).

28. N. Bushaw, J. Chen, H. LaFayette, C. E. Larson, N. Van Cleemput, Conjectured Bounds for the Independence Number of a Graph, submitted.

27. N. Bushaw, B. Conka, V. Gupta, A. Kierans, H. Lafayette, C. E. Larson, S. Loeb, K. McCall, A. Mulyar, C. Sullivan, S. Taylor, E. Wainright, E. Wilson, G. Wu, Bootstrap Percolation via Automated Conjecturing, submitted.

26. P. Brooks, D. Edwards, C.E. Larson, and N. Van Cleemput, Automated Conjecturing IV: Scientific Discovery and Classification, submitted.

25. N. Bushaw, C.E. Larson, N. Van Cleemput, Automated Conjectures for Graph Hamiltonicity, submitted.

24. L. Hutchinson, V. Kamat, C. E. Larson, S. Mehta, D. Muncy, and N. Van Cleemput, Automated Conjecturing VI: Domination Number of Benzenoids, MATCH, 2018.

23. C. E. Larson and N. Van Cleemput, Automated Conjecturing I: Fajtlowicz's Dalmatian Heuristic Revisited (Extended Abstract), Proceedings of the 2017 International Joint Conference on Artificial Intelligence (IJCAI-17), Melbourne, pp. 5015-5019.

22. C. E. Larson and N. Van Cleemput, Automated Conjecturing III: Property-relations Conjectures, Annals of Mathematics and Artificial Intelligence 81(3) (2017) 315-327.

21. C. E. Larson and N. Van Cleemput, Automated Conjecturing I: Fajtlowicz's Dalmatian Heuristic Revisited, Artificial Intelligence 231 (2016) 17-38.

20. C. E. Larson and N. Van Cleemput, Forcing Independence, Croatica Chemica Acta, Vol.86, No.4, Dec. 2013, 469-475.

19. G. Brinkmann, C. E. Larson, J. Souffriaua, N. Van Cleemput, Construction of Planar 4-connected Triangulations, Ars Mathematica Contemporanea, Vol 9, No 2 (2015).

18. C. E. Larson, L. Mitchell, B. Lins, Graphs of Unitary Matrices and Positive Definite Zero Forcing, Reports on Mathematical Physics (ROMP), 72 (3), December 2013, 311--320.

17. R. Gera, C. E. Larson, C. Rasmussen, and R. Pepper, Independence in Function Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing (JCMCC 94) 2015, 301--312.

16. D. J. Klein and C. E. Larson, Eigenvalues of Saturated Hydrocarbons, Journal of Mathematical Chemistry 51(6) 2013, 1608--1618.

15. C. E. Larson and R. Pepper, Three Bounds for the Independence Number of a Graph, Bulletin of the Institute of Combinatorics and its Applications 70, 2014, 86--96.

14. E. DeLaVina and C. E. Larson, A Parallel Algorithm for Computing the Critical Independence Number and Related Sets, Ars Mathematica Contemporanea 6(2) 2013, 237--245.

13. L. Eroh, R. Gera, C. Kang, C. E. Larson, and E. Yi, Domination in Functigraphs, Discussiones Mathematicae Graph Theory 32 (2012).

12. C. E. Larson and R. Pepper, Graphs with Equal Independence and Annihilation Numbers, Electronic Journal of Combinatorics, 18(1) 2011.

11. E. DeLaVina, C. E. Larson, R. Pepper, and B. Waller, A Characterization of Graphs where the Independence Number Equals the Radius, Graphs and Combinatorics 28 (2012) 315-332.

10. C. E. Larson, The Critical Independence Number and an Independence Decomposition, European Journal of Combinatorics 32(2), 2011, 294--300.

9. G. Abay-Asmeron, R. Hammack, C. E. Larson, D. T. Taylor, Notes on the independence number in the Cartesian product of graphs, Discussiotnes Mathematica Graph Theory 31(1), 2011, 25--35.

8. E. DeLaVina, C. Larson, R. Pepper and B. Waller, On total domination and support vertices of a tree, AKCE International Journal of Graphs and Combinatorics, 7 (1), 2010, 85--95.

7. E. DeLaVina, C. E. Larson, R. Pepper, and B. Waller, Graffiti.pc on the 2-domination number of a graph, Congressus Numerantium 203, 2010, 15--32.

6. G. Abay-Asmerom, R. Hammack, C. E. Larson, and D. Taylor, Direct Product Factorization of Bipartite Graphs with Bipartite-Switching Involutions, SIAM Journal on Discrete Mathematics 20(4), 2010, 2042--2052.

5. E. DeLaVina, C. E. Larson, R. Pepper, and B. Waller, Graffiti.pc on the total domination number of a tree, Congressus Numerantium 195, 2009, 5--18.

4. C. E. Larson, A Note on Critical Independence Reductions, Bulletin of the Institute of Combinatorics and its Applications 5, 2007, 34--46.

3. C. E. Larson, A Survey of Research in Automated Mathematical Conjecture-making, in Graphs and Discovery, ed. by S. Fajtlowicz, P. W. Fowler, P. Hansen, M. F. Janowitz and F. S. Roberts, DIMACS, 2005, 297--318.

2. S. Fajtlowicz and C. E. Larson, Graph-theoretic Independence as a Predictor of Fullerene Stability, Chemical-Physics Letters, 377/5-6, 2003, 485--490.

1. C. E. Larson, Intelligent Machinery and Mathematical Discovery, Graph Theory Notes of the New York Academy of Science XLII, 2002, 8--17.

Books

2. R. Gera, S. Hedetniemi, C. E. Larson, eds., Graph Theory: Favorite Conjectures and Open Problems, Springer, 2016.

1. C. E. Larson, Graph Theoretic Independence and Critical Independent Sets (dissertation), 2008.

Other

8. N. Bushaw, C. E. Larson, N. Van Cleemput, Automated Conjecturing VII: The Graph Brain Project & Big Mathematics (arXiv preprint).

7. K. Chilakamarri, M. F. Khan, C. E. Larson, and C. J. Tymczak, Self-similar Graphs (arXiv preprint).

6. C. E. Larson, VCU's New Anti-Science Curriculum, Richmond Times-Dispatch, Mar. 18, 2018, (long version).

5. C. E. Larson, How to Respond to Obscure Writing, August 2016.

4. C. E. Larson, Inequality and an American Principle of Fairness, August 2016.

3. C. E. Larson, In Defense of Being Offensive: Our Responsibility as Intellectuals, July 2016.

2. C. E. Larson, School success requires more than good intentions, Richmond Times-Dispatch, Sept. 13, 2015.

1. C. E. Larson, Technology, Education and the Single-Salary Schedule, Notices of the American Mathematical Society, May 2006, 525.

Online Talks

3. Chomp & New Heuristics for Interpretable Machine Learning, IJCAI-2021 invited talk, Aug. 23, 2021 (poster)

2. Conjecturing-Based Computational Discovery of Patterns in Data INFORMS Annual Meeting, Nov., 2020.

1. Automated Conjecturing for Proof Discovery, University of Western Ontario, 2016.