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/throttling of a graph or sign pattern.

Catalog of graphs listing minimum rank


Throttling for the game of Cops and Robbers  on graphs
J. Breen, B. Brimkov, J. Carlson, L. Hogben, K.E. Perry, C. Reinhart. Discrete Math., 341 (2018) 2418–2430.
[PDF preprint]

Restricted power domination and zero forcing problems 
C. Bozeman, B. Brimkov, C. Erickson, D. Ferrero, M. Flagg, L. Hogben.  [PDF preprint]

Families of graphs with maximum nullity equal to zero forcing number
J.S. Alameda, E. Curl, A. Grez, L. Hogben, O'N. Kingston, A. Schulte, D. Young, M. Young. Special Matrices 6 (2018), 56 - 67 [PDF preprint]

Applications of analysis to the determination of the minimum number of distinct eigenvalues of a graph
B. Bjorkman, L. Hogben, S. Ponce, C. Reinhart, T. Tranel.  To appear in Pure Appl. Funct. Anal. [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. To appear in Discrete Appl. Math. [PDF preprint]

The inverse eigenvalue problem of a graph: Multiplicities and minors
W. Barrett, S Butler, S.M. Fallat, H.T. Hall, L Hogben, J.C.-H. Lin, B.L. Shader, M. Young.
[PDF preprint]

The relationship between k-forcing and k-power domination.
  
D. Ferraro, L. Hogben, F.H.J. Kenter, M. Young. Discrete Math. 341 (2018), 1789–1797. [PDF preprint]


Note on Nordhaus-Gaddum problems for power domination 
K.F. Benson, D. Ferrero, M. Flagg, V. Furst, L. Hogben, V. Vasilevska.  Discrete Appl. Math. in press [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, 34 (2017), 736-641.  [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]

Zero forcing and power domination for graph products
 
K.F. Benson, D. Ferrero, M. Flagg, V. Furst, L. Hogben, V. Vasilevska, B. Wissman.   Australasian J. Comnbinatorics 70 (2018), 221-235.  [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 J. 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, 27 (2014), 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. 27 (2014), 444-457 [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
 
M. Catral, A. Cepek, L. Hogben, M. 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
L. Hogben, M. Huynh, S. Meyer, N. Kingsley, S. Walker, M. 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
J. Ekstrand, C. Erickson, D. Hay, L. Hogben, J. Roat. Electonic Journal of Linear Algebra 23 (2012) 79-87
[PDF]

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

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

Parameters related to tree-width, zero forcing, and maximum nullity of a graphs
F. Barioli, W. Barrett, S. Fallat, H.T. Hall,  L. Hogben, B. Shader, P. van den Driessche, H.
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
C.
Edholm, L. Hogben, M. Huynh, J, LaGrange, D. Row. Linear Algebra and its Applications 436 (2012): 4352–4372 [PDF ]

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


Zero forcing parameters and minimum rank problems
F. Barioli, W. Barrett, S. Fallat, H.T. Hall,  L. Hogben, B. Shader, P. van den Driessche, H.
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
H.T.
Hall, L. Hogben, R. Martin, B. Shader. Linear Algebra and its Applications 433 (2010) 101–117 [PDF ]

Techniques for determining the minimum rank of a small graph
L. DeLoss, J. Grout, L. Hogben, T. McKay, J. mith, G. 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
L. Hogben. Linear Algebra and its Applications 432 (2010) 1961–1974
[PDF ]

Generic maximum nullity of a graph

L. Hogben, B. 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
F. Barioli, S.M. Fallat, H.T. Hall, D. Hershkowitz, L. Hogben, H. van der Holst, B. Shader.
  Electronic Journal of Linear Algebra 18 (2009): 126-145.

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

Orthogonal representations, minimum rank, and graph complements
L. Hogben, 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
A. Berman, S. Friedland, L. Hogben, U. Rothblum, B. 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
S. Fallat, L. Hogben.
  Linear Algebra and its Applications, 426 (2007) 558-582. [PDF]

Minimum Rank of a Tree over an Arbitrary Field
N.L. Chenette, S.V. Droms, L. Hogben, R. Mikkelson, O. Pryporova) 
  Electronic Journal of Linear Algebra 16 (2007): 183-186.

Forbidden Minors for the Class of Graphs G with xi(G) <= 2
L. Hogben, H. 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
A. Chowdhury, L. Hogben, J. Melancon, R. Mikkelson, 
Linear Algebra and its Applications 418 (2006) 380-393 pdf .

Minimum Rank and Maximum Eigenvalue Multiplicity of Symmetric Tree Sign Patterns
L.M. DeAlba, T. Hardy, I.R. Hentzel, L. Hogben, A. 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

F. Barioli, S.M. Fallat, L. Hogben.  
Electronic Journal of Linear Algebra 13 (2005), 387-404

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

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

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

Papers on distance spectra and 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.  Linear Algebra Appl., 497 (2016), 66-87. 
[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.
To appear in Electron. J. Linear Algebra.  [PDF preprint]

Papers on eventually nonnegative matrices and their sign patterns

Note on the Jordan form of  an irreducible eventually nonnegative matrix
L. Hogben, B.-S. Tam, U. Wilson.  Note on the Jordan form of an irreducible eventually nonnegative matrix.  Electron. J. Linear Algebra, 30 (2015), 279-285. [link to PDF]


Potentially eventually exponentially positive sign patterns
M. Archer, M. Catral, C. Erickson, R. Haber, L. Hogben, X. Martinez-Rivera, A. Ochoa.  Involve 6 (2013): 261-271. PDF preprint

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

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

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

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

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

Sign patterns that allow eventual positivity
A. Berman, M. Catral, L.M. DeAlba, A. Elhashash, F. Hall, L. Hogben, I.-J. Kim, D. Olesky, P. Tarazaga, M. Tsatsomeros, P. van den Driessche.
Electronic Journal of Linear Algebra  19 (2010): 108-120.

Sign patterns that require eventual positivity or require eventual nonnegativity
E. Ellison, L. Hogben, M. 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. 
W. 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 Graph
M. 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 forcing
D
. 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. 
D. Burgarth, D. D'Alessandro, L. Hogben, S. Severini, M. 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
C. Qui, N. Vaswani, B. Lois, L. Hogben.  IEEE Transactions on Information Theory, 60 (2014): 5007 – 5039.   [PDF preprint

Papers on positivity and matrix completion problems

SPN graphs and rank-1 CP-completable graphs. 
L. Hogben, N. Shaked-Monderer. [PDF preprint]

The Q-Matrix Completion Problem
L.M. DeAlba, L. Hogben, B.K.Sarma. 
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.

Linear Algebra & Spectral Graph Theory Sites


 
Leslie Hogben's Homepage June 30, 2018