Research Papers etc.

Leslie Hogben
Dio Lewis Holl Chair in Applied Mathematics and Professor, Department of Mathematics, Iowa State University
Associate Director for Diversity, American Institute of Mathematics

The primary emphasis of my current research is in linear algebra, combinatorics, and applications of linear algebra to other fields.  A long time ago I worked in ring theory (Jordan and other nonassociative algebras and connections between ring theory and universal algebra).

I am the Dio Lewis Holl Chair in Applied Mathematics at Iowa State University mad the Associate Director for Diversity of the American Institute of Mathematics.

I am the Secretary/Treasurer of the International Linear Algebra Society.


I am the editor of Handbook of Linear Algebra and an editor of Recent Trends in Combinatorics.

I am an associate editor of Linear Algebra and its Applications and an associate editor of Electronic Journal of Linear Algebra.

There is an active ISU Discrete Mathematics Research Cluster that operates the Discrete Mathematics Seminar meeting weekly during the academic year and graduate students are encouraged to attend.  I frequently lead the ISU Combinatorial Matrix Theory Research Group, sometimes as an REU (research experiences for undergraduates) or EGR (early graduate research) group.


Papers on minimum rank/maximum nullity/Colin De Verdiere parameters/zero forcing/power domination/propagation time of a graph or sign pattern.

Catalog of graphs listing minimum rank



Applications of analysis to the determination of the minimum number of distinct eigenvalues of a graph
Beth Bjorkman, Leslie Hogben, Scarlitte Ponce, Carolyn Reinhart, Theodore Tranel.  [PDF preprint]

Throttling positive semidefinite zero forcing propagation time on graphs
J. Carlson, L. Hogben, J. Kritschgau, K. Lorenzen, M.S. Ross, V. Valle Martinez.  [PDF preprint]

The inverse eigenvalue problem of a graph: Multiplicities and minors
Wayne Barrett, Steve Butler, Shaun M. Fallat, H. Tracy Hall, Leslie Hogben, Jephian C.-H. Lin, Bryan L. Shader, Michael Young.
[PDF preprint]

The relationship between k-forcing and k-power domination.
   D. Ferraro, L. Hogben, F.H.J. Kenter, M. Young.   [PDF preprint]

Note on Nordhaus-Gaddum problems for power domination  K.F. Benson, D. Ferrero, M. Flagg, V. Furst, L. Hogben, V. Vasilevska [PDF Preprint]

Multi-part Nordhaus-Gaddum type problems for tree-width, Colin de Verdi\`ere type parameters, and Hadwiger number.    L. Hogben, J.C.-H. Lin, M. Young.  [PDF Preprint]

Note on power propagation time and lower bounds for power domination number.   D. Ferraro, L. Hogben, F.H.J. Kenter, M. Young.   J. Combinatorial Optimization.   [PDF Preprint]

Generalizations of the Strong Arnold Property and  the minimum number of distinct eigenvalues of  a graph  W. Barrett, S. Fallat, H. T. Hall,  L. Hogben, J. C.-H. Lin, B.L. Shader Electron. J. Combinatorics, 24 (2017) P2.40 (28 pages). [link to PDF]

Power domination
and zero forcing  K.F. Benson, D. Ferrero, M. Flagg, V. Furst, L. Hogben, V. Vasilevska, B. Wissman [PDF Preprint]

Fractional Zero Forcing via Three-color Forcing Games  L. Hogben, K. Palmowski, D. Roberson, M. Young.  Discrete Appl. Math., 213 (2016),  114-129.  [PDF preprint]

Orthogonal representations, projective rank, and fractional minimum positive semidefinite rank: connections and new directions  L. Hogben,  K. Palmowski, D. E. Roberson, S. Severini. Electronic Journal of Linear Algebra 32 (2017), 98-115 [PDF]

Zero forcing propagation time on oriented graphs.  A. Berliner, C. Bozeman, S. Butler, M. Catral, L. Hogben, B. Kroschel, J.C.-H. Lin, N. Warnberg, M. Young.   Discrete Appl. Math. 224 (2017), 45-59. [PDF preprint]

Nordhaus-Gaddum Problems for Colin de Verdiere Type Parameters, Variants of Tree-width, and Related Parameters.   Leslie Hogben.   Recent Trends in Combinatorics, IMA Volume in Mathematics and its Applications, Springer, 2016. [PDF]

Minimum rank of graphs with loops.  C. Bozeman, AV. Ellsworth, L. Hogben, J.C.-H. Lin, G. Maurer, K. Nowak, A. Rodriguez, J. Strickland. Electron. J. Linear Algebra  27 (2014):  907 – 934. [PDF]

Path cover number, maximum nullity, and zero forcing number of oriented graphs and other simple digraphs.  A. Berliner, C. Brown, J. Carlson, N. Cox, L. Hogben, J. Hu, K. Jacobs, K. Manternach, T. Peters, N. Warnberg, M. Young Involve 8 (2015): 147 – 167. [PDF]

Minimum rank with zero diagonal.  C. Grood, J. Harmse, L. Hogben, T.J. Hunter, B. Jacob, A. Klimas, S. McCathern Electronic Journal of Linear Algebra, Volume 27, pp. 458-477 [PDF]

The maximum nullity of a complete subdivision graph is equal to its zero forcing number.  W. Barrett, S, Butler, M. Catral, S. Fallat, H.T. Hall, L. Hogben, M. Young   Electronic Journal of Linear Algebra. [PDF]

Minimum rank, maximum nullity, and zero forcing number for simple digraphs. A. Berliner, M. Catral, L. Hogben, M. Huynh, K. Lied, M. Young.  Electronic Journal of Linear Algebra, 26 (2013), 762-780 [PDF]

Note on Nordhaus-Gaddum problems for Colin de Verdiere type parameters. 
W. Barrett, S. Fallat, H. T. Hall, L. Hogben. Electronic Journal of Combinatorics, 20 (2013) P56 (9 pages). [PDF]

Zero forcing number, maximum nullity, and path cover number of subdivided graphs.
  Minerva Catral, Anna Cepek, Leslie Hogben, My Huynh, Kirill Lazebnik, Travis Peters, Michael Young Electronic Journal of Linear Algebra, 23 (2012), 906-922 [PDF]

Propagation time for zero forcing on a graph.  Leslie Hogben, My Huynh, Sarah Meyer, Nicole Kingsley, Shanise Walker, Michael Young.   Discrete Applied Mathematics 160 (2012) 1994-2005. [PDF]

Positive semidefinite zero forcing number.   J.Ekstrand, C. Erickson,  H.T. Hall, D. Hay, R. Johnson, N. Kingsley, S. Osborne, T. Peters, J. Roat, A. Ross, D. Row, N. Warnberg, M. Young).    Linear Algebra and its Applications, 439 (2013): 1862 – 1874. [PDF ]

Note on positive semidefinite maximum nullity and positive semidefinite zero forcing number of partial 2-trees.   (with Ekstrand, Erickson, Hay, Roat). Electonic Journal of Linear Algebra 23 (2012) 79-87 [PDF]

On the Graph Complement Conjecture for minimum rank (with Barioli, Barrett, Fallat, Hall,  van der Holst Linear Algebra and its Applications. 436 (2012): 4373–4391 [PDF]

Minimum rank of certain families of graphs
(with Almodovar, DeLoss, Hogenson, Murphy, Peters, Ramirez) Involve: a journal of mathematics 3 (2010): 371-392. [PDF]

Parameters related to tree-width, zero forcing, and maximum nullity of a graphs (with Barioli, Barrett, Fallat, Hall,  Shader, van den Driessche, van der Holst). Journal of Graph Theory 72 (2013), 146 – 177 [PDF ]

Vertex and edge spread of zero forcing number, maximum nullity, and 
minimum rank of a graph
(with Edholm, Huynh, LaGrange, Row) Linear Algebra and its Applications 436 (2012): 4352–4372 [PDF ]

A note on minimum rank and maximum nullity of  sign patterns Electron. J. Linear Algebra 22 (2011) 203-213.

Zero forcing parameters and minimum rank problems (with Barioli, Barrett, Fallat, Hall,  Shader, van den Driessche, van der Holst). Linear Algebra and its Applications 433 (2010) 401–411. [PDF]

Expected values of parameters associated with the minimum rank of a graph (with Hall, Martin, Shader) Linear Algebra and its Applications 433 (2010) 101–117 [PDF ]

Techniques for determining the minimum rank of a small graph (with DeLoss, Grout, McKay, Smith, Tims)   Linear Algebra and its Applications 432 (2010) 2995–3001.[PDF ]

Minimum rank of skew-symmetric matrices described by a graph (IMA-ISU research group on minimum rank, 16 authors)  Linear Algebra and its Applications 432 (2010) 2457–2472 [PDF

Minimum rank problems Linear Algebra and its Applications 432 (2010) 1961–1974 [PDF ]

Generic maximum nullity of a graph
(with Bryan Shader)
Linear Algebra and its Applications 432 (2010) 857–866 [PDF]

Universally optimal matrices and field independence of the minimum rank of a graph (with DeAlba, Grout, Mikkelson, Rasmussen) Electronic Journal of Linear Algebra 18 (2009): 403-419.

On the minimum rank of not necessarily symmetric matrices: A preliminary study
(with Barioli, Fallat, Hall, Hershkowitz, van der Holst, Shader)
  Electronic Journal of Linear Algebra 18 (2009): 126-145.

An upper bound for the minimum rank of a graph (with Berman, Friedland, Rothblum, Shader)   [PDFLinear Algebra and its Applications 429/7 (2008) 1629 – 1638.

Orthogonal representations, minimum rank, and graph complements Linear Algebra and its Applications, 428/11-12 (2008) 2560-2568. [PDF preprint]

Zero forcing sets and the minimum rank  of graphs (AIM minimum rank - special graphs work group, 18 authors)  Linear Algebra and its Applications, 428/7 (2008) 1628–1648. [PDF].

Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers (with Berman, Friedland, Rothblum, Shader). Electronic Journal of Combinatorics, 15/1 (2008) R 25 (19 pages).  Appendix

The Minimum Rank of Symmetric Matrices Described by a Graph: A Survey (with Shaun Fallat)   Linear Algebra and its Applications, 426 (2007) 558-582. [PDF]

Minimum Rank of a Tree over an Arbitrary Field (with Nathan L. Chenette, Sean V. Droms, Rana Mikkelson and Olga Pryporova)   Electronic Journal of Linear Algebra 16 (2007): 183-186.

Forbidden Minors for the Class of Graphs G with xi(G) <= 2 (with van der Holst)  Linear Algebra and its Applications 423 (2007) 42-52  [PDF preprint ].

Rational Realization of Maximum Eigenvalue Multiplicity of Symmetric Tree Sign Patterns (with Chowdhury, Melancon, Mikkelson),  Linear Algebra and its Applications 418 (2006) 380-393 pdf .

Minimum Rank and Maximum Eigenvalue Multiplicity of Symmetric Tree Sign Patterns (with DeAlba, Hardy, Hentzel, Wangsness),  Linear Algebra and its Applications 418 (2006) 389-415 PDF

A variant on the graph parameters of Colin de Verdiere: Implications to the minimum rank of graphs
(with Barioli, Fallat)  
Electronic Journal of Linear Algebra 13 (2005), 387-404

Spectral Graph Theory and the Inverse Eigenvalue Problem of a Graph Electronic Journal of Linear Algebra 14 (2005): 12-31

On the Difference between Maximal Multiplicity and Path Cover Number for Tree-like Graphs   (with Barioli and Fallat)  Linear Algebra and its Applications, 409 (2005) 13-31[PDF ]

Computation of Path Cover Number and Minimal Rank for Graphs   (with Barioli and Fallat)  Linear Algebra and its Applications 392 (2004):289-303.     [PDF ]

Papers on spectral graph theory

On the distance spectra of graphs    G. Aalipour, A. Abiad, Z. Berikkyzy, J. Cummings, J. De Silva, W. Gao, K. Heysse, L. Hogben, F.H.J. Kenter, J.C.-H. Lin, M. Tait.    [PDF preprint]

Proof of a conjecture of Graham and Lovasz concerning unimodality of coefficients of the distance characteristic polynomial of a tree 
G. Aalipour, A. Abiad, Z. Berikkyzy, L. Hogben, F.H,J. Kenter, J.C.-H. Lin, M.Tait. 
[PDF preprint]

Papers on eventually nonnegative matrices and their sign patterns

Note on the Jordan form of  an irreducible eventually nonnegative matrix Leslie Hogben and Ulrica Wilson. 

Potentially eventually exponentially positive sign patterns (with Archer, Catral, Erickson, Haber, Martinez-Rivera, Ochoa).  Involve 6 (2013): 261-271. PDF preprint

Eventual properties of matrices Leslie Hogben and Ulrica Wilson. Electronic Journal of Linear Algebra, 23 (2012), 953-965.

Sign patterns that allow strong eventual nonnegativity (with Catral, Erickson, Olesky, van den Driessche) Electronic Journal of Linear Algebra 23 (2012): 1-10.

Constructions of potentially eventually positive sign patterns with reducible positive part (with Archer, Catral, Erickson, Haber, Martinez-Rivera, Ochoa).   Involve 4 (2011): 405-410   PDF preprint

Eventually cyclic matrices and a test for strong eventual nonnegativity Electronic Journal of Linear Algebra 19 (2010): 129-140.

Sign patterns that require or allow power-positivity (with Catral, Olesky, van den Driessche) Electronic Journal of Linear Algebra 19 (2010): 121-128.

Sign patterns that allow eventual positivity (with Berman, Catral, DeAlba, Elhashash, Hall, Kim, Olesky, Tarazaga, Tsatsomeros, van den Driessche)  Electronic Journal of Linear Algebra  19 (2010): 108-120.

Sign patterns that require eventual positivity or require eventual nonnegativity (with Ellison and Tsatsomeros) Electronic Journal of Linear Algebra 19 (2010): 98-107.

Papers on principal rank characteristic sequences

The enhanced principal rank characteristic sequence for Hermitian matrices.  S. Butler, M. Catral, H.T. Hall, L. Hogben, X. Martinez-Rivera, B. Shader, And P. van den Driessche. The enhanced principal rank characteristic sequence for Hermitian matrices. To appear in Electronic J Linea Algebra [PDF preprint]

The enhanced principal rank characteristic sequence.
  S. Butler, M. Catral, S. Fallat, T. Hall, L. Hogben, P. van den Driessche, M. YoungLinear Algebra and its Applications 498 (2016) 181-200 [PDF preperint]

The principal rank characteristic sequence over various fields.  Wayne Barrett, S. Butler, M. Catral, S. Fallat, T. Hall, L. Hogben, P. van den Driessche, M. Young  Linear Algebra and its Applications 459 (2014), 222–236 [PDF preperint]

Papers on applications of linear algebra and combinatorics

Note on von Neumann and Renyi entropies of a GraphM. Dairyko, L. Hogben, J.C.-H. Lin, J. Lockhart, D. Roberson, S. Severini, M. Young. Linear Algebra Appl.  521 (2017), 240-253 [PDF]

Logic circuits from zero forcingD. Burgarth, V. Giovanetti, L. Hogben, S. Severini, M. Young.  Natural Computing 14 (2015), 485–490.  [PDF]

Zero forcing, linear and quantum controllability for systems evolving on networks.  Daniel Burgarth, Domenico D'Alessandro, Leslie Hogben, Simone Severini, Michael Young.   IEEE Transactions on Automatic Control 58 (2013): 2349 – 2354 [PDF preprint - this material in this link is copyright 2013 by IEEE]

Recursive Robust PCA or Recursive Sparse Recovery in Large but Structured Noise Chenlu Qui, Namrata Vaswani, Brian Lois, Leslie Hogben.  IEEE Transactions on Information Theory, 60 (2014): 5007 – 5039.   [PDF preprint

Papers on matrix completion problems

The Q-Matrix Completion Problem (with DeAlba and Sarma) to appear in  Electronic Journal of Linear Algebra Electronic Journal of Linear Algebra 18 (2009): 176-191. 

The Copositive Matrix Completion Problem: Unspecified Diagonal,  Linear Algebra and its Applications  420 (2007) 160-162.    [ PDF preprint]

On completion problems for various classes of P-matrices 
(with Bowers, Evers, Shaner, Snider, Wangsness)  Linear Algebra and its Applications   413 (2006) 342-354 [ PDF preprint]

The Copositive Matrix Completion Problem (with Johnson and Reams)   Linear Algebra and its Applications 408 (2005) 207-211 [PDF preprint ]

Relationships between the Completion Problems for Various Classes of Matrices
Proceedings of the 2003 SIAM Conference on Applied Linear Algebra   [ PDF ]

The (Weakly) Sign Symmetric P-Matrix Completion Problems (with DeAlba, Hardy, Wangsness)
 Electronic Journal of Linear Algebra 10 (2003): 257-271 

The Nonnegative P0 -Matrix Completion Problem ( with Choi, DeAlba, Kivunge, Nordstrom, Shedenhelm)
Electronic Journal of Linear Algebra 10 (2003): 46-59 

Matrix Completion Problems for Pairs of Related Classes of Matrices
    Linear Algebra and its Applications 373 (2003): 13-29  [ PDF preprint ]

The P0-Matrix Completion Problem ( with Choi, DeAlba, Maxwell, Wangsness)
    Electronic Journal of Linear Algebra 9 (2002): 1-20 

The Symmetric M-Matrix and Symmetric Inverse M-Matrix Completion Problems
 Linear Algebra and its Applications 353 (2002): 159-167   [ PDF preprint ]

Graph Theoretic Methods for Matrix Completion Problems
     Linear Algebra and its Applications 328 (2001): 161-202  [PDF preprint ]

Completions of P-Matrix Patterns (with Luz DeAlba)
        Linear Algebra and its Applications 319 (2000): 83-102  [  PDF preprint ]

Inverse M-Matrix Completions of Patterns Omitting Some Diagonal Positions
          Linear Algebra and its Applications 313 (2000): 173-192. 

Completions of Inverse M-Matrix Patterns
Linear Algebra and its Applications 282 (1998): 145-160.  

Completions of M-Matrix Patterns
Linear Algebra and its Applications 285 (1998): 143-152.

Papers on crossing numbers

Crossing numbers of complete tripartite and balanced complete multipartite graphs.  Ellen Gethner, Leslie Hogben, Bernard Lidicky, Florian Pfender, Amanda Ruiz, Michael YoungJ Graph Theory 84 (2017) 552–565 [PDF preprint]

Papers on rainbow arithmethic progressions

Rainbow arithmetic progressions.  Steve Butler, Craig Erickson, Leslie Hogben, Kirsten Hogenson, Lucas Kramer, Richard L. Kramer, Jephian Chin-Hung Lin, Ryan R. Martin, Derrick Stolee, Nathan Warnberg, Michael Young. J Combintorics 7 (2016), 595-626 [PDF preprint]

Papers on Partition Regular matrices

A linear algebraic view of partition regular matrices (with Jillian McLeod)
        Linear Algebra and its Applications 433 (2010) 1809–1820  [  PDF preprint ]

Papers on Spectrally Arbitrary sign/nonzero Patterns

Spectrally Arbitrary Patterns: Reducibility and the 2n Conjecture (with DeAlba,  Hentzel, McDonald, Mikkelson, Pryporova, Shader, Vander Meulen)  Linear Algebra and Its Applications, 423 (2007)  262-276. [PDF preprint]

Papers on Stable and Convergent Matrices

Multiplicative Perturbations of Stable and Convergent Operators, (with Bryan Cain, Luz M. DeAlba, and Charles R. Johnson)
Linear Algebra and Its Applications 268 (1998): 151-169.


Recent Talks

Generalizations of the Strong Arnold Property and the Inverse Eigenvalue Problem of a Graph
  Joint Mathematics Meetings, Atlanta, January 2017 PDF slides

Multi-part Nordhaus-Gaddum type problems for tree-width, Colin de Verdiere type parameters, and Hadwiger number
  AMS Central Section, Minneapolis, October 2016 PDF slides

Distance Spectra of Graphs
  47th Southeastern International Conference on Combinatorics, Graph Theory & Computing (plenary), March 2016 PDF slides

Crossing numbers of complete tripartite and balanced complete multipartite graphs
  University of Puerto Rico, Rio Piedras Campus, February 2015 PDF slides

Minimum rank problems
  Bates College, November 2013 PDF slides

Average minimum rank of graphs
  16th International Linear Algebra Society Conference, Pisa, June 2010 PDF slides

Minimum Rank Problems: Recent Developments
  15th International Linear Algebra Society Conference (plenary), Cancun, June 2008 PDF slides

Combinatorial Matrix Theory and Spectral Graph Theory
  International Conference on Algebra and Related Topics (ICART 2008), Bangkok, May 2008 PDF slides


Linear Algebra & Spectral Graph Theory Sites

Linear Algebra Conferences (out of date)
 
Leslie Hogben's Homepage Feb. 20, 2017