Publications
      T. S. Michael   (updated October 2012)

• Publications are listed by topic on this page.

• Publications may also be viewed in reverse CHRONOLOGICAL order.

• Disclaimer for research papers posted: Material contained herein is made available for the purpose of peer review and discussion and does not necessarily reflect the views of the Department of the Navy or the Department of Defense.

General Discrete Mathematics

• T. S. Michael,
   How to Guard an Art Gallery and Other Discrete Mathematical Adventures. (book)
   Johns Hopkins University Press, Baltimore, 2009.

Linear Algebra and Matrices in Combinatorics

• Ilhan Hacioglu and T. S. Michael,
  The p-ranks of residual and derived skew Hadamard designs,
  Discrete Mathematics, 311 (2011) 2216-2219.

• Elizabeth Doering, T. S. Michael, and Bryan Shader,
  Even and odd tournament matrices with minimum rank over finite fields,
  Electronic Journal of Linear Algebra,  22 (2011) 363-377.

• T. S. Michael,
  Ryser's embedding problem for Hadamard matrices,
  Journal of Combinatorial Designs 14 (2006) 41-51.

• T. S. Michael and Thomas Quint,
  Optimal strategies for node selection games: skew matrices and symmetric games,
  Linear Algebra and Its Applications 412 (2006) 77-92.

• T. S. Michael,
  The rigidity theorems of Hamada and Ohmori, revisited, 
  in Coding Theory and Cryptography: From the Geheimschreiber and Enigma to Quantum Theory.  
  (Annapolis, MD, 1998) 175-179, Springer, Berlin, 2000.     pdf
  MR 2001c:05035

• T. S. Michael and W. D. Wallis,
  Skew-Hadamard matrices and the Smith normal form,
  Designs, Codes, and Cryptography, 13 (1998) 173-176.

• T. S. Michael,
  The p-ranks of skew Hadamard designs,
  Journal of Combinatorial Theory, Series A, 73 (1996) 170-171.

• T. S. Michael,
  The ranks of tournament matrices,
  American Mathematical Monthly, 102 (1995) 637-639.

• T. S. Michael,
  The decomposition of the complete graph into three isomorphic strongly regular graphs,
  Congressus Numerantium, 85 (1991) 177-183.

Tiling 

• Richard J. Bower and T. S. Michael,
   Packing boxes with bricks,
   Mathematics Magazine, 79 (2006), 14-30.

• Richard J. Bower and T. S. Michael,
  When can you tile a box with translates of two given rectangular bricks?,
  Electronic Journal of Combinatorics 11 (2004) Note 7, 9 pages (electronic).
  PDF file (6 June 2004: corrects index typo in Theorem 8')

Art Gallery Theorems and Computational Geometry

• T. S. Michael and Val Pinciu,
  Guarding orthogonal prison yards: an upper bound,
  Congressus Numerantium,to appear

• T. S. Michael,
  Guards, galleries, fortresses, and the octoplex,
  College Math Journal, 42 (2011) 191-200.

• T. S. Michael and Val Pinciu,
   Art gallery theorems and triangulations
   DIMACS Educational Module Series, 2007, 18 pp (electronic 07-1)

• T. S. Michael and Val Pinciu,
  Guarding the guards in art galleries,
  Math Horizons, 14 (2006), 22-23, 25.

• T. S. Michael and Val Pinciu,
  Art gallery theorems for guarded guards,
  Computational Geometry 26 (2003) 247-258.   DVI File

• T. S. Michael and Val Pinciu,
  Multiply guarded guards in orthogonal art galleries,
  Lecture Notes in Computer Science 2073, pp 753-762,
  in: Proceedings of the International Conference on Computer Science, San Francisco, Springer, 2001.

Graph Decompositions

• T. S. Michael,
  Impossible decompositions of complete graphs into three Petersen subgraphs,
  Bulletin of the Institute of Combinatorics and Its Applications 39 (2003) 64-66
  
  (See also publication on strongly regular graph decompositions in linear algebra section.)

Extremal Graph Theory

• T. S. Michael,
  Cycles of length 5 in triangle-free graphs: a sporadic counterexample to a characterization of equality
  Bulletin of the Institute of Combinatorics and Its Applications, to appear

Permanents

• Suk-Geun Hwang, Arnold R. Kraeuter, and T. S. Michael,
  An upper bound for the permanent of a nonnegative matrix,
  Linear Algebra and Its Applications 281 (1998) 259-263.  MR 99k:15011
  * First Corrections: Linear Algebra and Its Applications 300 (1999), no. 1-3,  1-2  MR 2001f:15006

• Richard A. Brualdi, John L. Goldwasser, and T. S. Michael,
  Maximum permanents of matrices of zeros and ones,
  Journal of Combinatorial Theory, Series A, 47 (1988) 207-245.

Proximity Graphs and Sphere of Influence Graphs

• T. S. Michael and Thomas Quint,
  Sphericity, cubicity, and edge clique covers of graphs,
  Discrete Applied Mathematics 154 (2006) 1309-1313.  (erratum June 2009)

• T. S. Michael and Thomas Quint,
  Sphere of influence graphs and the L-Infinity metric,
  Discrete Applied Mathematics  127 (2003) 447-460.

• T. S. Michael and Thomas Quint,
  Sphere of influence graphs in general metric spaces,
  Mathematical and Computer Modelling, 29 (1999) 45-53. 
  MR 2000c:05106

• T. S. Michael and Thomas Quint,
  Sphere of influence graphs: a survey,
  Congressus Numerantium, 105 (1994) 153-160.

• T. S. Michael and Thomas Quint,
  Sphere of influence graphs: edge density and clique size,
  Mathematical and Computer Modelling, 20 (1994) 19-24.

Matrices with Prescribed Row and Column Sums
(Degree Sequences of Graphs)

• T. S. Michael ,
  Signed degree sequences and multigraphs,
  Journal of Graph Theory 41 (2002) 101-105.

• T. S. Michael,
  Lower bounds for graph domination by degrees,
  pp 789-800 in Graph Theory, Combinatorics, and Algorithms: Proceedings of the Seventh Quadrennial International Conference on the Theory and Applications of Graphs, Y. Alavi and A. Schwenk (eds.), Wiley, New York, 1995.

• T. S. Michael,
  The structure matrix of the class of r-multigraphs with a prescribed degree sequence,
  Linear Algebra and Its Applications, 183 (1993) 155-177.

• T. S. Michael,
  The structure matrix and a generalization of Ryser's maximum term rank formula,
  Linear Algebra and Its Applications, 145 (1991) 21-31.
• Richard A. Brualdi and T. S. Michael,
  The class of matrices of zeros, ones and twos with prescribed row and column sums,
  Linear Algebra and Its Applications, 114(115) (1989) 181-198.
• Richard A. Brualdi and T. S. Michael,
  The class of 2-multigraphs with a prescribed degree sequence,
  Linear and Multilinear Algebra, 24 (1989) 81-102.

Independence Sequences of Graphs

• T. S. Michael  and William N. Traves ,
  Independence sequences of well-covered graphs: non-unimodality and the roller-coaster conjecture,
  Graphs and Combinatorics  19  (2003) 403-411.

Knots and Graphs

• Brenda Johnson, Mark E. Kidwell, and T. S. Michael,
  Intrinsically knotted graphs have at least 21 edges,
  Journal of Knot Theory and Its Ramifications, 19 (2010) 1423-1429.

Pedagogy

• T. S. Michael and Val Pinciu,
   Art gallery theorems and triangulations
   DIMACS Educational Module Series, 2007, 18 pp (electronic 07-1)

• T. S. Michael,
  Alumni Profiles: United States Naval Academy,
  Math Horizons 12, February 2004.

• T. S. Michael and Aaron Stucker,
  Mathematical pitfalls with equivalence classes,
  PRIMUS, 3 (1993) 331-335.