Current Research and Publications

Books

  • Chris Godsil and Karen Meagher. Erdős-Ko-Rado Theorems: Algebraic Approaches.
    You can order this book from Cambridge University press.

    • Journal Publications

    1. Karen Meagher, A.S. Razafimahatratra and Pablo Spiga.
      On triangles in derangement graphs submitted to JCTA Aug 2020. Available at arXiv

    2. Joseph S. Alameda, Franklin Kenter, Karen Meagher, Michael Young.
      An upper bound for the k-power domination number in r-uniform hypergraphs. Submitted to Discrete Mathematics. April 2020. Available at arXiv

    3. Karen Meagher and A.S. Razafimahatratra.
      2-intersecting permutations Electronic Journal of Combinatorics April 2020. Available at arXiv

    4. Shaun Fallat, Karen Meagher, Mahsa N. Shirazi.
      The Erd\H{o}s-Ko-Rado theorem for 2-intersecting families of perfect matchings. submitted to Algebraic Combinatorics Aug. 2020 Available at arXiv

    5. Khawla Almuhtaseb, Shaun Fallat, Karen Meagher, Shahla Nasserasr, Mahsa N. Shirazi, A. S. Razafimahatratra.
      Weakly Hadamard Diagonalizable Graphs. To appear Linear Algebra and Its Applications. Sept. 2020.

    6. K. Meagher and P. Sin.
      All 2-transitive groups have the EKR-module property. JCTA. 177 (2021). Available at arXiv

    7. Adm, S.~Fallat, K.~Meagher, S.~Nasserasr, S.~Plosker, B.~Yang.
      Achievable Multiplicity partitions in the inverse eigenvalue problem of a graph. to appear in Special Matrices Available at arXiv

    8. Kokkala J, Meagher K, Naserasr R, Nurmela K, Ostergard P, Stevens B.
      Bounds, structure, and classification of small strength-2 covering arrays. To appear: Journal of Combinatorial Designs. June 2019. Available at arXiv

    9. Susanna Fishel, Glenn Hurlbert, Vikram Kamat and Karen Meagher.
      Erdős-Ko-Rado theorems on the weak Bruhat lattice. Discrete Applied Mathematics 266 (2019) 65--75 Available at arXiv

    10. Karen Meagher
      An Erdős-Ko-Rado theorem for the group PSU(3, q)
      Designs, Codes, and Cryptography Available at arXiv

    11. Mohammad Adm, Ryan Bergen, Ferdinand Ihringer, Sam Jaques, Karen Meagher, Alison Purdy, Boting Yang
      Ovoids of Generalized Quadrangles of Order (q,q^2−q) and Delsarte Cocliques in Related Strongly Regular Graphs
      J. Combin. Des. 26 (2018), no. 5, 249--263.
      Available at arXiv

    12. Aras Erzurumluo\u{g}lu, Karen Meagher, and David A. Pike.
      Brushing Number and Zero-Forcing Number of Graphs and their Line Graphs.
      To appear Graphs and Combinatorics. Available at arXiv .

    13. Shaun Fallat, Karen Meagher, Abolghasem Soltani and Boting Yang. Compressed Cliques Graphs, Clique Coverings and Positive Zero Forcing.
      Theoret. Comput. Sci. 734 (2018), 119--130..
      Available at arXiv.

    14. Ryan Bergen, Shaun Fallat, Adam Gorr, Ferdinand Ihringer, Karen Meagher, Alison Purdy, Boting Yang and Guanglong Yu
      Infection in Hypergraphs.
      Discrete Appl. Math. 237 (2018), 43--56.
      Available at arXiv.

    15. Ferdinand Ihringer and Karen Meagher. Mikl\'os-Manickam-Singhi Conjectures on Partial Geometries.
      Des. Codes Cryptogr. 86 (2018), no. 6, 1311--1327.
      Available at arXiv.

    16. Chris Godsil and Karen Meagher. An algebraic proof of the Erdős-Ko-Rado theorem for intersecting families of perfect matchings.
      Ars Math. Contemp. 12 (2017), no. 2, 205--217.
      Available at arXiv.

    17. Karen Meagher, Pablo Spiga and Pham Huu Tiep. An Erdős-Ko-Rado theorem for finite $2$-transitive groups.
      To appear European Journal of Combinatorics, 2016.
      Available at arXiv.

    18. Peter Borg and Karen Meagher. The Katona cycle proof of the Erdős-Ko-Rado theorem and its possibilities.
      To appear Godsil 65 special issue of Journal of Algebraic Combinatorics, 2014

    19. Shaun Fallat, Karen Meagher and Boting Yang. On the Complexity of the Positive Semidefinite Zero Forcing Number
      Linear Algebra and its Applications, 491(15) 101--122, 2016
      Available at arXiv.

    20. Karen Meagher and Alison Purdy. Intersection theorems for multisets.
      European Journal of Combinatorics, 52, 120--135, 2016.
      Available at arXiv.

    21. Peter Borg and Karen Meagher. Intersecting generalised permutations.
      Australasian Journal of Combinatorics. 61, 147--155, 2015
      Available at arXiv.

    22. Adam Dyck and Karen Meagher. An Erdős-Ko-Rado theorem for subset partitions.
      Involve, a Journal of Mathematics 8(1)119--127, 2015.
      Available at arXiv.

    23. Bahman Ahmadi and Karen Meagher. The Erdős-Ko-Rado property for some permutation groups.
      The Australasian Journal of Combinatorics. vol.61, p.23--41, 2015.
      Available at arXiv .

    24. Karen Meagher and Pablo Spiga. An Erdős-Ko-Rado theorem for the derangement graph of $PGL_3(q)$ acting on the projective plane.
      SIAM Journal on Discrete Mathematics 28(2) 918--941, 2014.
      Available at arXiv.

    25. Fatemeh Alinaghipour Taklimi, Shaun Fallat and Karen Meagher. On the Relationships between Zero Forcing Numbers and Certain Graph Coverings.
      Special Matrices 2, 30--45, 2014.
      Available at arXiv.

    26. Bahman Ahmadi and Karen Meagher. The Erdős-Ko-Rado property for some 2-transitive groups.
      The Annals of Combinatorics. 19(4), 621--640, 2015.
      Available at arXiv .

    27. Bahman Ahmadi, Fatemeh Alinaghipour, Michael S. Cavers, Shaun Fallat, Karen Meagher and Shahla Nasserasr. Minimum number of distinct eigenvalues of graphs.
      Electronic Journal of Linear Algebra. 26, Article 45. pp. 21, 2014.
      Available at arXiv .

    28. Bahman Ahmadi and Karen Meagher. A new proof for the Erdős-Ko-Rado Theorem for the alternating group.
      Discrete Mathematics. 324(6) 28--40, 2014.
      available at arXiv.

    29. R. Bailey, J. Caceres, D. Garijo, A. Gonzalez, A. Marquez, K. Meagher and M. Puertas. Resolving sets in Johnson and Kneser graphs.
      European Journal of Combinatorics 34(4) 736--751, 2013
      available at arXiv.

    30. P. C. Li and Karen Meagher. Sperner Partition Systems. To appear Journal of Combinatorial Designs 21(7), 267--279, 2013.
      available at arXiv.

    31. Bahman Ahmadi, Fatimeh Alinaghipour, Shaun Fallat, Y. Fan, Karen Meagher and Shahla Nasserasr.
      The minimum rank of universal adjacency matrices. To appear Linear Algebra and its Applications. 437(8), 2064--2076, 2012.
      available at arXiv.

    32. Karen Meagher and Alison Purdy.
      An Erdős-Ko-Rado theorem for multisets. Electronic Journal of Combinatorics 18(1) Paper 220, 8 pp, 2011.
      available arXiv.

    33. Robert Bailey, Andrea Burgess, Michael Cavers and Karen Meagher.
      Generalized covering designs and clique coverings. Journal of Combinatorial Designs 19, 378-406, 2011.
      available at JCD .

    34. Robert Bailey and Karen Meagher.
      On the metric dimension of Grassman graphs. Discrete Math and Theoretical Computer Science, 13(4):97-104, 2011.
      available at arXiv.

    35. Karen Meagher and Pablo Spiga.
      An Erdős-Ko-Rado theorem for the derangement graph of $PGL(2,q)$ acting on the projective line. Journal of Combinatorial Theory Series A. 118(2), 532--544, 2011.
      available at arXiv.

    36. Chris Godsil and Karen Meagher.
      Multiplicity-free representations of the symmetric group.
      Annals of Combinatorics, 13(4):463-490, 2009.
      available at arXiv

    37. Chirs Godsil and Karen Meagher.
      A new proof of the Erdős-Ko-Rado theorem for intersecting families of permutations. European Journal of Combinatorics, 30(2):404-414, 2009.
      available at arXiv.

    38. Karen Meagher, Lucia Moura and Latifa Zekaoui.
      Mixed covering arrays on graphs. Journal of Combinatorial Designs, 15(5):393-404, 2007.

    39. Karen Meagher, Lucia Moura and Brett Stevens.
      A Sperner-type theorem for set-partition systems, Electronic Journal of Combinatorics, 12(1) Note 20, 6 pp. (electronic), 2005.

    40. Karen Meagher and Lucia Moura.
      Erdős-Ko-Rado theorems for uniform set-partition systems. Electronic Journal of Combinatorics, 12(1) Research Paper 40, 12 pp. (electronic), 2005.

    41. Karen Meagher and Brett Stevens.
      Covering arrays on graphs. Journal of Combinatorial Theory, Series B, 95(1):134-151, 2005.

    42. Karen Meagher and Brett Stevens.
      Group construction of covering arrays. Journal of Combinatorial Designs, 13(1):70-77, 2005.

      43. Other Publications

    43. Karen Meagher and Irene Sciriha. Graphs that have a weighted adjacency matrix with spectrum $\{\lambda_1^{n-2}, \lambda_2^2\}$.
      (This paper will not appear in a journal, since the results are too similar to work in other recent papers.)
      Available at arXiv.
    44. Karen Meagher and Alison Purdy. The exact bound for the Erdős-Ko-Rado theorem for t-cycle-intersecting permutations.
      available at arXiv.
      This paper will not be published in a journal since a 2011 paper by V. M. Blinovsky uses a similar method to get essentially the same result.
    45. Karen Meagher. Covering arrays on graphs: qualitative independence graphs and extremal set-partition theory. Ph.D. thesis, University of Ottawa, 177 pages, Sept. 2005.
      available at www.arxiv.org/pdf/math.CO/0701553.
    46. Karen Meagher. Group Construction of Covering Arrays --- Part 2. Technical Report, 5 pages, Jan. 2005.
    47. Karen Meagher. Convolution estimates with Orlicz spaces. Masters thesis, University of Waterloo, 130 pages, May 1997.

      48. Graduate Students

      Current

      Completed

      (2014) Alison Purdy (Ph.D.) Thesis title: Variations on a Theorem of Erdös, Ko and Rado.
      (2013) Fatemeh Alinaghipour, Ph.D. Thesis title: Zero Forcing Sets for Graphs.
      (2013) Bahman Ahmadi, Ph.D. Thesis title: Maximum Intersecting Families of Permutations.
      (2010) Alison Purdy, Masters. Thesis title: The Erdős-Ko-Rado Theorem for Intersecting Families of Permutations. Alison's Thesis

      Some Old Presentations and Other Projects

      Group Construction of Covering Arrays

    48. This is part two of the my paper Group Constructions of Covering Array. The first paper used an exhaustive search in the construction, this search is replaced a hill-climbing algorithm. In this paper new bounds for covering arrays on larger alphabets are given. ( PS , PDF )

      49. Presentation for Colloque de Science Mathematique du Quebec

    49. Covering arrays on Graphs presentation ( PDF)

      50. Presentation for LaCIM

    50. "Covering Arrays on Graphs and Connections to Extremal Combinatorics " ( PDF)

      51. Presentation for the University of Waterloo Algebraic Combinatorics Seminar July 7 2005

    51. "Covering Arrays and Covering Arrays on Graphs" ( PDF)

      52. Presentation for Regina

    52. "Covering Arrays on Graphs: extremal partition theory and qualitative independence graphs" ( PDF)

      53. Presentation for Ottawa

    53. "Two Approaches to the Study of Covering Arraypublications.html s" ( PDF)

      54. Presentations for the Canadam Conference

    54. "Covering Arrays on Graphs" ( PDF)
    55. "Set-Partitions and Association Schemes" ( PDF)

      56. Presentations for Discrete Math Day and Ottawa Graph Theory Conference

    56. "Applications of Graph Theory to Covering Arrays" ( PDF)
    57. "A Mulit-Partite Erdős-Ko-Rado Theorem" ( PDF)

      58. [back to home page]

      Last modified: Mon Sep 9 14:55:10 EDT