# Glenn Hurlbert, Ph.D.

Professor

## Education

- Ph.D., Mathematics, Rutgers University (Ronald Graham, adviser)
- M.A., Mathematics, State University of New York at Stony Brook (Joel Spencer, adviser)
- B.S., Mathematics (Computer Science minor), Wake Forest University

## Research

Hurlbert has published over 80 articles, chapters and books, and received the Editor's Choice Best Research Paper Award from the Journal of Discrete Mathematics. His research has been supported by the National Science Foundation, the National Security Agency, the J. William Fulbright Program, the Simons Foundation, the Mathematical Association of America, the Eisenhower Foundation, the Banff International Research Station, and Motorola.

Hurlbert is a Fulbright Scholar and Arizona State University (ASU) Emeritus President’s Professor who has won the Distinguished Teaching Award from the Southwest Section of the Mathematical Association of America, the Charles Wexler Teaching Award from the ASU School of Mathematics & Statistical Sciences, the ASU Faculty Achievement Award for Student Mentoring, the Professor of the Year Runner-Up from the ASU Parents Association, the Texty Award from the Text and Academic Authors Association.

### Interests

- Graph pebbling
- Universal cycles
- Extremal set theory
- Combinatorial optimization
- Combinatorial bijections
- General graph theory
- Discrete mathematics
- Mathematical education

## Visiting Positions

- National University of Argentina, San Luis
- National University of Argentina, La Plata
- Institute for Defense Analysis, La Jolla
- Center for Mathematical Research, Barcelona
- Autonomous University of Barcelona
- Institute for Defense Analysis, Princeton
- The Johns Hopkins University
- Dartmouth College
- Vanderbilt University
- Federal University of Rio de Janeiro
- Alfréd Rényi Institute of Mathematics, Budapest

## Select Publications

### Books and Chapters

- Graph Pebbling, chapter in Handbook of Discrete and Combinatorial Mathematics (2nd ed.), K. Rosen, J. Michaels, W. Goddard, J. Gross, J. Grossman and D. Shier, eds., CRC Press, Boca Raton, 2018.
- Connections in Discrete Mathematics: A Celebration of the Work of Ron Graham (ed. with S. Butler and J. Cooper), Cambridge Univ. Press, Cambridge, 2018.
- Graph Pebbling, chapter in Handbook of Graph Theory (2nd ed.), Discrete Mathematics and its Applications, J. Gross, J. Yellen, and P. Zhang, eds. CRC Press, Boca Raton, 2014.
- Linear Optimization: The Simplex Workbook, Undergraduate Texts in Mathematics. Springer, New York, 2010.
- Proceedings of the Workshop on Generalizations of de Bruijn Cycles and Gray Codes (ed. with B. Jackson and B. Stevens), held at the Banff International Research Station, Banff, December 4–9, 2004, Discrete Math. 309 (2009), no. 17.

### Articles

- Cops and robbers pebbling in graphs (with N. Clarke and J. Forkin), submitted.
- Thresholds for 0-sums with small cross numbers in abelian groups (with N. Bushaw), submitted.
- Cup stacking in graphs (with P. Fay and M. Tennant), submitted.
- On the pebbling numbers of some snarks (with M. Adauto, M. da Cruz, C. de Figueiredo, and D. Sasaki), submitted.
- On the Holroyd-Talbot conjecture for sparse graphs (with P. Frankl), Discrete Math. 347 (2023), no. 1, 113742.
- Pebbling in powers of paths (with L. Alcón), Discrete Math. 346 (2023), no. 5, 113315.
- On intersecting families of independent sets in trees (with V. Kamat), Discrete Appl. Math. 321 (2022), 4–9.
- Ronald Lewis Graham (1935--2020), Notices Amer. Math. Soc., 68 (2021), no. 11, 1931–1950.
- Graph Pebbling: A blend of graph theory, number theory, and optimization (with F. Kenter), Notices Amer. Math. Soc., 68 (2021), no. 11, 1900–1913. (Also: Chinese translation in Mathematical Advances in Translation, Academy of Mathematics and Systems Science (Chinese Academy of Sciences) 41 (2022), no. 3, 216--234.)
- Erdős-Ko-Rado theorems on the weak Bruhat lattice (with S. Fishel, V. Kamat and K. Meagher), Discrete Appl. Math. 266 (2019), 65–75.
- New injective proofs of the Erdős-Ko-Rado and Hilton-Milner theorems (with V. Kamat), Discrete Math., 341 no. 6 (2018), 1749–1754.
- The weight function lemma for graph pebbling, J. Combin. Opt., 34 no. 2 (2017), 343–361.
- 1-Overlap cycles for Steiner triple systems (with V. Horan), Des. Codes Cryptogr. 72 no. 3 (2014), 637–651.
- Pebbling in split graphs (with L. Alcón and M. Gutierrez), SIAM J. Discrete Math. 28 no. 3 (2014), 1449–1466.
- Erdős-Ko-Rado theorems for chordal graphs and trees (with V. Kamat), J. Comb. Th. (A) 118 no. 3 (2011), 829–841.
- An application of graph pebbling to zero-sum sequences in abelian groups (with S. Elledge), Integers: Elec. J. Combin. Number Th. 5 no. 1 (2005), #A17.
- Thresholds for families of multisets, with an application to graph pebbling (with A. Bekmetjev, G. Brightwell and A. Czygrinow), Discrete Math. 269 (2003), no. 1-3, 21–34.
- A note on graph pebbling (with A. Czygrinow, H. Kierstead, and W. T. Trotter), Graphs and Combin. 18 (2002), 219–225.
- Spanning trees of bounded degree (with A. Czygrinow, G. Fan, H. Kierstead, and W. T. Trotter), Elec. J. Comb. 8 (2001), no.1, Research Paper 33, 12 pages.
- On the existence of De Bruijn tori with 2 x 2 windows (with C. Mitchell and K. Paterson), J. Comb. Th. (A) 76 (1996), no.2, 213–230.
- The dimension of interior levels of the boolean lattice (with A. Kostochka and L. Talysheva), Order 11 (1994), no.1, 29–40.
- On the De Bruijn torus problem (with G. Isaak), J. Comb. Th. (A) 64 (1993), no.1, 50–62.

## Affiliations

- American Mathematical Society
- Center for Discrete Mathematics and Theoretical Computer Science
- Institute for Combinatorics and its Applications
- Institute for Operations Research and Management Science
- Mathematical Association of America
- MAA Project Next Fellow
- Society for Industrial and Applied Mathematics
- Textbook and Academic Authors Association