Current Research and Publications


Books

Chris Godsil and Karen Meagher. Erdős-Ko-Rado Theorems: Algebraic Approaches. This book is available now, you can order it from Cambridge University press.

Journal Publications

  1. Aras Erzurumluo\u{g}lu, Karen Meagher, and David A. Pike. Brushing Number and Zero-Forcing Number of Graphs and their Line Graphs.
    Submitted to Discrete Applied Mathematics, Sept. 2016. Available at arXiv .
  2. Shaun Fallat, Karen Meagher, Abolghasem Soltani and Boting Yang. Compressed Cliques Graphs, Clique Coverings and Positive Zero Forcing.
    Submitted to Theoretical Computer Science, Oct. 2016.
    Available at arXiv.
  3. Ryan Bergen, Shaun Fallat, Adam Gorr, Ferdinand Ihringer, Karen Meagher, Alison Purdy, Boting Yang and Guanglong Yu
    Infection in Hypergraphs.
    Submitted to Journal of Graph Theory, July 28, 2016 Available at arXiv.
  4. Ferdinand Ihringer and Karen Meagher. Mikl\'os-Manickam-Singhi Conjectures on Partial Geometries.
    Submitted to Combinatorica, 2016.
    Available at arXiv.
  5. Chris Godsil and Karen Meagher. An algebraic proof of the Erdős-Ko-Rado theorem for intersecting families of perfect matchings.
    To appear ARS Mathematica Contemporanea, 2016.
    Available at arXiv.
  6. 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.
  7. 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
  8. 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.
  9. Karen Meagher and Alison Purdy. Intersection theorems for multisets.
    European Journal of Combinatorics, 52, 120--135, 2016.
    Available at arXiv.
  10. Peter Borg and Karen Meagher. Intersecting generalised permutations.
    Australasian Journal of Combinatorics. 61, 147--155, 2015
    Available at arXiv.
  11. 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.
  12. 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 .
  13. 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.
  14. 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.
  15. 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 .
  16. 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 .
  17. 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.
  18. 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.
  19. P. C. Li and Karen Meagher. Sperner Partition Systems. To appear Journal of Combinatorial Designs 21(7), 267--279, 2013.
    available at arXiv.
  20. 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.
  21. 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.
  22. 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 .
  23. 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.
  24. 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.
  25. Chris Godsil and Karen Meagher. Multiplicity-free representations of the symmetric group.
    Annals of Combinatorics, 13(4):463-490, 2009.
    available at arXiv
  26. 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.
  27. Karen Meagher, Lucia Moura and Latifa Zekaoui. Mixed covering arrays on graphs. Journal of Combinatorial Designs, 15(5):393-404, 2007.
  28. 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.
  29. 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.
  30. Karen Meagher and Brett Stevens. Covering arrays on graphs. Journal of Combinatorial Theory, Series B, 95(1):134-151, 2005.
  31. Karen Meagher and Brett Stevens. Group construction of covering arrays. Journal of Combinatorial Designs, 13(1):70-77, 2005.

  32. Other Publications

  33. 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.
  34. 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.
  35. 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.
  36. Karen Meagher. Group Construction of Covering Arrays --- Part 2. Technical Report, 5 pages, Jan. 2005.
  37. Karen Meagher. Convolution estimates with Orlicz spaces. Masters thesis, University of Waterloo, 130 pages, May 1997.

  38. 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

  39. 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 )
  40. Presentation for Colloque de Science Mathematique du Quebec

  41. Covering arrays on Graphs presentation ( PDF)
  42. Presentation for LaCIM

  43. "Covering Arrays on Graphs and Connections to Extremal Combinatorics " ( PDF)
  44. Presentation for the University of Waterloo Algebraic Combinatorics Seminar July 7 2005

  45. "Covering Arrays and Covering Arrays on Graphs" ( PDF)
  46. Presentation for Regina

  47. "Covering Arrays on Graphs: extremal partition theory and qualitative independence graphs" ( PDF)
  48. Presentation for Ottawa

  49. "Two Approaches to the Study of Covering Arraypublications.html s" ( PDF)
  50. Presentations for the Canadam Conference

  51. "Covering Arrays on Graphs" ( PDF)
  52. "Set-Partitions and Association Schemes" ( PDF)
  53. Presentations for Discrete Math Day and Ottawa Graph Theory Conference

  54. "Applications of Graph Theory to Covering Arrays" ( PDF)
  55. "A Mulit-Partite Erdős-Ko-Rado Theorem" ( PDF)
  56. [back to home page]

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