Research Papers etc.
Leslie Hogben
Professor, Department of Mathematics, and Associate Dean, College of Liberal Arts and Sciences, Iowa State University
Associate Director for Diversity, American Institute of Mathematics
This page is outdated. See ArXiv for recent papers.
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).
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
Product throttling
S.E. Anderson, K.L. Collins, D. Ferrero,
L. Hogben, C. Mayer, A.N. Trenk, S. Walker. In Recent
Trends in Graph Theory and Applications, Springer, 2021. [arxiv]
Product throttling for power domination
S.E. Anderson, K.L. Collins, D. Ferrero, L. Hogben, C. Mayer, A.N. Trenk, S. Walker. [arxiv]
Reconfiguration graphs of zero forcing sets
J. Geneson, R. Haas, L. Hogben. [arxiv]
Skew throttling
E. Curl, J. Geneson, L. Hogben. Australasian J . Combinatorics, 78 (2020), 117-190. [arxiv]
Using Markov chains to determine expected propagation time for probabilistic zero forcing.
Y. Chan, E. Curl, J. Geneson, L. Hogben, K. Liu, I. Odegard, M.S. Ross. Electronic J. Linear Algebra 36 (2020) 318-333
Cop throttling number: Bounds, values, and variants.
A. Bonato, J. Breen, B. Brimkov, J. Carlson, S. English, J. Geneson, L. Hogben, K.E. Perry. To appear in J. Comb.[arXiv]
Propagation time for probabilistic zero forcing
J. Geneson, L. Hogben. [arXiv]
Rigid linkages and partial zero forcing
D. Ferrero, M. Flagg, H.T. Hall, L. Hogben, J.C.-H. Lin, S.A. Meyer, S. Nasserasr, B. Shader. Electron. J. Combinatorics, 26 (2019) P2.43
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. [arXiv]
Restricted power domination and zero forcing problems
C. Bozeman, B. Brimkov, C. Erickson, D. Ferrero, M. Flagg, L. Hogben. J. Combinatorial Optimization, 37 (2019), 935–956. [arXiv]
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 in ISU DR]
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. Pure Appl. Funct. Anal. 3 (2018), 537--563. [arXiv]
Throttling positive semidefinite zero forcing propagation time on graphs
J. Carlson, L. Hogben, J. Kritschgau, K. Lorenzen, M.S. Ross, S. Selken, V. Valle Martinez. Discrete Appl. Math. 254 (2019), 33–46. [arXiv]
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. [arXiv]
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. [arXiv]
Note on Nordhaus-Gaddum problems for power domination
K.F. Benson, D. Ferrero, M. Flagg, V. Furst, L. Hogben, V. Vasilevska. Discrete Appl. Math., 251 (2018), 103--113. [arXiv]
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. [arXiv]
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. [arXiv]
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).
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. Combinatorics 70 (2018), 221-235. [arXiv]
Fractional Zero Forcing via Three-color Forcing Games
L. Hogben, K. Palmowski, D. Roberson, M. Young. Discrete Appl. Math., 213 (2016), 114-129. [arXiv]
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.
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 in ISU DR]
Nordhaus-Gaddum Problems for Colin de Verdiere Type Parameters, Variants of Tree-width, and Related Parameters
L. Hogben. Recent Trends in Combinatorics, IMA Volume in Mathematics and its Applications, Springer, 2016. [PDF in ISU DR]
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.
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 in ISU DR]
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.
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.
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.
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).
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.
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.
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.
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.
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.
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 in ISU DR]
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 in ISU DR]
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.
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.
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.
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.
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.
Minimum rank
problems
L. Hogben. Linear Algebra and its Applications 432 (2010) 1961–1974.
Generic
maximum nullity of a graph
L. Hogben, B. Shader. Linear Algebra and its Applications 432 (2010) 857–866
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. Linear
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.
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.
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.
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.
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.
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
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.
Papers on distance spectra and spectral graph theory
Spectra of variants of distance matrices of graphs and digraphs: a survey. To
L. Hogben, C. Reinhart. To appear in La Matematica. [arxiv]
Spectral theory of products of digraphs.
M. Catral, L. Ciardo, L. Hogben, C. Reinhart. Electronic J. Linear Algebra 36 (2020)744-763
Graphs that are cospectral for the distance Laplacian
B. Brimkov, K. Duna, L. Hogben, K. Lorenzen, C. Reinhart, S.-Y. Song, M. Yarrow. Electronic J. Linear Algebra 36 (2020) 334-351
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.
[arXiv]
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. Electron. J. Linear Algebra 34 (2018) 373–380.
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.
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 in ISU DR]
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 in ISU DR]
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 positivity and matrix
completion problems
SPN graphs.
L. Hogben, N. Shaked-Monderer. Electronic Journal of
Linear
Algebra 35 (2019): 376-386.
The Q-Matrix
Completion
Problem
L.M. DeAlba, L. Hogben, B.K.Sarma. Electronic Journal of
Linear
Algebra 18 (2009): 176-191.
The
Copositive Matrix
Completion
Problem: Unspecified Diagonal
L. Hogben. Linear
Algebra and its Applications 420 (2007) 160-162.
On completion problems for
various classes of P-matrices
Bowers, Evers, Shaner, Snider, Wangsness) Linear
Algebra and its Applications 413 (2006) 342-354.
The Copositive Matrix
Completion
Problem
L.Hogben, C.R. Johnson,R.
Reams.
Linear Algebra and its Applications 408
(2005) 207-211
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
L.M. DeAlba, T. Hardy, L. Hogben, A. Wangsness.
Electronic
Journal of Linear Algebra 10 (2003): 257-271
The Nonnegative P0
-Matrix Completion Problem
J.Y. Choi, L.M. DeAlba, L. Hogben, B. Kivunge,
S. Nordstrom,
M. Shedenhelm.
Electronic
Journal of Linear Algebra 10 (2003): 46-59
Matrix Completion Problems
for
Pairs of Related Classes of Matrices
L. Hogben. Linear
Algebra and its Applications
373
(2003): 13-29
The P0-Matrix
Completion
Problem
J.Y. Choi, L.M. DeAlba, L. Hogben, M. Maxwell, A. Wangsness. Electronic
Journal of Linear Algebra 9 (2002): 1-20
The Symmetric M-Matrix and
Symmetric
Inverse M-Matrix Completion Problems
L. Hogben. Linear Algebra
and its Applications 353 (2002):
159-167
Graph Theoretic Methods for
Matrix
Completion Problems
L. Hogben. Linear
Algebra and its Applications 328 (2001):
161-202
Completions of P-Matrix
Patterns
Luz DeAlba, Leslie Hogben. Linear
Algebra and its Applications 319 (2000): 83-102
Inverse M-Matrix
Completions
of Patterns Omitting Some Diagonal Positions
L. Hogben. Linear Algebra and its Applications 313 (2000):
173-192.
Completions of Inverse
M-Matrix
Patterns
L. Hogben. Linear Algebra and its Applications
282
(1998): 145-160.
Completions of M-Matrix
Patterns
L. Hogben. Linear Algebra and its Applications 285
(1998): 143-152.
Papers on principal rank characteristic sequences
The sepr-sets of sign patterns.
L. Hogben, J.C.-H. Lin, D. D. Olesky, P. van den Driessche. Linear Multilinear Algebra. ,.8 (2020), 2044-2068. [arXiv]
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. Electronic J Linear Algebra 32 (2017), 58-75.
The enhanced principal rank characteristic sequence.
S. Butler, M. Catral, S. Fallat, T. Hall, L. Hogben, P. van den Driessche, M. Young. Linear
Algebra and its Applications 498 (2016) 181-200 [PDF in ISU DR]
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.
Papers on applications of linear algebra and graph theory
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 [arXiv]
Logic circuits from zero forcing.
D. Burgarth, V. Giovanetti, L. Hogben, S. Severini, M. Young. Natural Computing 14 (2015), 485–490. [arXiv]
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 [arXiv
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. [arXiv - the material in this link is copyright 2014 by IEEE]
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 Young. J Graph Theory 84 (2017) 552–565 [arXiv]
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 [arXiv]
Papers on Partition Regular matrices
A linear algebraic view of partition regular matrices
L. Hogben, J. McLeod.
Linear
Algebra and its Applications 433 (2010) 1809–1820
Papers on Spectrally
Arbitrary sign/nonzero Patterns
Spectrally Arbitrary Patterns:
Reducibility and the 2n Conjecture
L.M. DeAlba,
I.R. Hentzel, L. Hogben, J.J. McDonald, R. Mikkelson, O. Pryporova, B. Shader, K. Vander Meulen. Linear
Algebra and
Its
Applications, 423 (2007) 262-276.
Papers on Stable and
Convergent
Matrices
Multiplicative Perturbations
of
Stable and Convergent Operators,
Bryan Cain, Luz M. DeAlba, Leslie Hogben, Charles R. Johnson. Linear Algebra and Its Applications 268
(1998): 151-169.
Slides from some recent plenary talks
- The Inverse Eigenvalue Problem of a Graph and Zero Forcing, 22nd ILAS Conference, July 11, 2019, Rio de Janeiro, Brazil
- Throttling for Cops & Robbers, zero forcing, and power domination, GRASCan2019, August 6, 2019, Toronto, Canada
