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 and Andriaherimanana Sarobidy Razafimahatratra.
      The intersection density of cubic arc-transitive graphs with 2-arc-regular full automorphism group equal to PGL 2 (q). to appear Combinatorial Theory, 2025.

    2. Karen Gunderson, Karen Meagher, Joy Morris, Venkata Raghu Tej Pantangi, Mahsa N. Shirazi.
      Robustness of Erdős--Ko--Rado theorems on permutations and perfect matchings. to appear Random Structures & Algorithms. 36 pages, Jan 2025.

    3. Karen Gunderson, Karen Meagher, Joy Morris and Venkata Raghu Tej Pantangi.
      Induced forests in some distance-regular graphs, Discrete Appl. Math. 346 (2024), 290–300. https://arxiv.org/abs/2301.05207

    4. Jozefien D'haeseleer, Karen Meagher, Venkata Raghu Tej Pantangi.
      Cameron-Liebler sets in permutation groups. To appear Algebraic combinatorics Jan 2024. https://arxiv.org/abs/2308.08254

    5. Shaun Fallat, Neha Joshi, Roghayeh Maleki, Karen Meagher, Seyed Ahmad Mojallal, Shahla Nasserasr, Mahsa N. Shirazi, Andriaherimanana Sarobidy Razafimahatratra, Brett Stevens.
      The q-Analogue of Zero Forcing for Certain Families of Graphs. Discrete Appl. Math. 348 (2024), 91–104. https://arxiv.org/abs/2306.01138

    6. Karen Meagher and A.S. Razafimahatratra.
      On the Intersection Density of the Kneser Graph K(n, 3). European J. Combin. 118 (2024), Paper No. 103910, 15 pp.

    7. Karen Meagher, Mahsa Shirazi, Brett Stevens.
      An Extension of the Erdős-Ko-Rado Theorem to uniform set partitions. Ars Mathematica Contemporanea. 23 (2023) 21pp.

    8. Allen Herman, Neha Joshi, Karen Meagher.
      Fusions of the generalized Hamming scheme on a strongly-regular graph Graphs and Combinatorics 38, Article number: 150 (2022) 28 pp

    9. Karen Meagher and A.S. Razafimahatratra.
      Some Erdős-Ko-Rado results for linear and affine groups of degree two. Art Discrete Appl. Math. 6 (2023), no. 1, Paper No. 1.05, 30 pp.

    10. Joseph S. Alameda, Franklin Kenter, Karen Meagher, Michael Young.
      An upper bound for the k-power domination number in r-uniform hypergraphs. Discrete Mathematics. 345:11 (2022) 9 pp.

    11. Karen Meagher, A. Sarobidy Razafimahatratra.
      The Erd˝os-Ko-Rado theorem for 2-pointwise and 2-setwise intersecting permutations. Electron. J. Combin. 28 (2021), no. 4, Paper No. 4.10, 21 pp.

    12. Shaun Fallat, Karen Meagher, Mahsa N. Shirazi.
      The Erdős-Ko-Rado theorem for 2intersecting families of perfect matchings. Algebraic Combinatorics (2021), no. 4, 575–598.

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

    14. 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

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

    16. 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

    17. 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.

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

    19. 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

    20. 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

    21. 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

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

    23. 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

    24. 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 .

    25. 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.

    26. 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.

    27. 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.

    28. 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.

    29. 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.

    30. 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

    31. 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.

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

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

    34. 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.

    35. 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 .

    36. 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.

    37. 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.

    38. 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 .

    39. 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 .

    40. 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.

    41. 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.

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

    43. 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.

    44. 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.

    45. 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 .

    46. 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.

    47. 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.

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

    49. 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.

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

    51. 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.

    52. 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.

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

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

    Other Publications

  • 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.
  • 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.
  • 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.
  • Karen Meagher. Group Construction of Covering Arrays --- Part 2. Technical Report, 5 pages, Jan. 2005.
  • Karen Meagher. Convolution estimates with Orlicz spaces. Masters thesis, University of Waterloo, 130 pages, May 1997.

    • Supervision

    Current

    1. Hermie Monterde -- PIMS Post-doctoral Fellow 10/2025 - present

    2. Alice Lacase-Masmonteil -- PIMS Post-doctoral Fellow 09/2024 - 08/2026

    3. Seyed Alireza Talebpour -- PhD student 01/2025 - present.

    Completed

    1. Cody Solie--NSERC USRA, 04/2024 - 08/2024 and 04/2025 - 08/2025.

    2. Rachel Evans -- MSc student 09/2022 - 04/2024.

    3. Venkata Raghu Tej Pantangi -- PIMS post-doctoral fellow

    4. Neha Joshi -- Mathematics PhD 2018 - 2022 (co-supervised with Dr. Herman)

    5. Mahsa Shirazi--Mathematics PhD 2018 - 2022 (co-supervised with Dr. Fallat)

    6. Sarobidy Razafimahatratra -- Mathematics PhD 2018 - 2022 (co-supervised with Dr. Fallat) Awarded the President's medal.

    7. Cody Antal -- USRA summer student 04/2021 - 08/2021 and 04/2022 - 08/2022

    8. Bennett Eidsness -- USRA summer student 04/2020 - 08/2020

    9. Dan Palmarin -- Mathematics Masters (co-supervised with Dr. Fallat) 06/18–12/20

    10. Adam Gorr -- Masters Student (co-supervised with Dr. Fallat) 07/16- 05/17

    11. Ferdinand Ihringer -- PIMS Post-Doctoral Fellow. 07/16 -07/17

    12. Sam Jaques -- USRA summer student Completed 04/2016 - 08/2016

    13. Alison Purdy (Ph.D.) -- Mathematics PhD 2010 - 2014
      Thesis title: Variations on a Theorem of Erdös, Ko and Rado.

    14. Fatemeh Alinaghipour -- Mathematics PhD 2009 - 2013 (co-supervised with Dr. Fallat)
      Ph.D. Thesis title: Zero Forcing Sets for Graphs.

    15. Bahman Ahmadi -- Mathematics PhD 2009 - 2013 Thesis title: Maximum Intersecting Families of Permutations.

    16. Alison Purdy -- Mathematics MSc 2008 - 2009 Thesis title: The Erdős-Ko-Rado Theorem for Intersecting Families of Permutations. Alison's Thesis

    17. Robert Bailey -- PIMS Post-doctoral Fellow ages ago.

    Some Old Presentations and Other Projects

    Group Construction of Covering Arrays

  • 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 )

    • Presentation for Colloque de Science Mathematique du Quebec

  • Covering arrays on Graphs presentation ( PDF)

    • Presentation for LaCIM

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

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

  • "Covering Arrays and Covering Arrays on Graphs" ( PDF)

    • Presentation for Regina

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

    • Presentation for Ottawa

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

    • Presentations for the Canadam Conference

  • "Covering Arrays on Graphs" ( PDF)
  • "Set-Partitions and Association Schemes" ( PDF)

    • Presentations for Discrete Math Day and Ottawa Graph Theory Conference

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

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    Last modified: May 28, 2026