Current Research and Publications
Books
Chris Godsil and Karen Meagher. ErdősKoRado Theorems: Algebraic Approaches.
This book is available now, you can order it from
Cambridge University press.
Journal Publications

Aras Erzurumluo\u{g}lu, Karen Meagher, and David A. Pike.
Brushing Number and ZeroForcing Number of Graphs and their Line
Graphs.
Submitted to Discrete Applied Mathematics, Sept. 2016.
Available at arXiv .

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.

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.

Ferdinand Ihringer and Karen Meagher.
Mikl\'osManickamSinghi Conjectures on Partial Geometries.
Submitted to Combinatorica, 2016.
Available at arXiv.

Chris Godsil and Karen Meagher.
An algebraic proof of the ErdősKoRado theorem for intersecting families of perfect matchings.
To appear ARS Mathematica Contemporanea, 2016.
Available at arXiv.

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

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

Shaun Fallat, Karen Meagher and Boting Yang. On the Complexity of the
Positive Semidefinite Zero Forcing Number
Linear Algebra and its Applications, 491(15) 101122, 2016
Available at arXiv.

Karen Meagher and Alison Purdy.
Intersection theorems for multisets.
European Journal of Combinatorics, 52, 120135, 2016.
Available at arXiv.

Peter Borg and Karen Meagher. Intersecting generalised permutations.
Australasian Journal of Combinatorics. 61, 147155, 2015
Available at arXiv.

Adam Dyck and Karen Meagher. An ErdősKoRado theorem for subset partitions.
Involve, a Journal of Mathematics 8(1)119127, 2015.
Available at arXiv.

Bahman Ahmadi and Karen Meagher. The ErdősKoRado property for some permutation groups.
The Australasian Journal of Combinatorics. vol.61, p.2341, 2015.
Available at arXiv .

Karen Meagher and Pablo Spiga. An ErdősKoRado theorem for the
derangement graph of $PGL_3(q)$ acting on the projective plane.
SIAM Journal on Discrete Mathematics 28(2) 918941, 2014.
Available at arXiv.

Fatemeh Alinaghipour Taklimi, Shaun Fallat and Karen Meagher.
On the Relationships between Zero Forcing Numbers and Certain Graph
Coverings.
Special Matrices 2, 3045, 2014.
Available at arXiv.

Bahman Ahmadi and Karen Meagher. The ErdősKoRado property for some 2transitive groups.
The Annals of Combinatorics. 19(4), 621640, 2015.
Available at arXiv .

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 .

Bahman Ahmadi and Karen Meagher. A new proof for the ErdősKoRado Theorem for the alternating group.
Discrete Mathematics. 324(6) 2840, 2014.
available at arXiv.
 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) 736751, 2013
available at arXiv.
 P. C. Li and Karen Meagher. Sperner Partition Systems.
To appear Journal of Combinatorial Designs 21(7), 267279, 2013.
available at arXiv.
 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), 20642076, 2012.
available at arXiv.
 Karen Meagher and Alison Purdy. An ErdősKoRado theorem for multisets.
Electronic Journal of Combinatorics 18(1) Paper 220, 8 pp, 2011.
available arXiv.
 Robert Bailey, Andrea Burgess, Michael Cavers and Karen Meagher. Generalized covering designs and clique coverings.
Journal of Combinatorial Designs 19, 378406, 2011.
available at JCD .
 Robert Bailey and Karen Meagher. On the metric dimension of Grassman graphs.
Discrete Math and Theoretical Computer Science, 13(4):97104, 2011.
available at arXiv.
 Karen Meagher and Pablo Spiga. An ErdősKoRado theorem for the
derangement graph of $PGL(2,q)$ acting on the projective line.
Journal of Combinatorial Theory Series A. 118(2), 532544, 2011.
available at arXiv.
 Chris Godsil and Karen Meagher. Multiplicityfree representations of the
symmetric group.
Annals of Combinatorics, 13(4):463490, 2009.
available at arXiv
 Chirs Godsil and Karen Meagher. A new proof of the ErdősKoRado theorem
for intersecting families of permutations. European
Journal of Combinatorics, 30(2):404414, 2009.
available at arXiv.
 Karen Meagher, Lucia Moura and Latifa Zekaoui. Mixed covering arrays on
graphs. Journal of Combinatorial Designs, 15(5):393404, 2007.
 Karen Meagher, Lucia Moura and Brett Stevens.
A Spernertype theorem for setpartition systems, Electronic
Journal of Combinatorics, 12(1) Note 20, 6 pp. (electronic), 2005.
 Karen Meagher and Lucia Moura. ErdősKoRado
theorems for uniform setpartition systems. Electronic
Journal of Combinatorics, 12(1) Research Paper 40, 12 pp. (electronic), 2005.
 Karen Meagher and Brett Stevens. Covering
arrays on graphs. Journal of Combinatorial Theory, Series B, 95(1):134151, 2005.
 Karen Meagher and Brett Stevens. Group construction of covering arrays.
Journal of Combinatorial Designs, 13(1):7077, 2005.
Other Publications

Karen Meagher and Irene Sciriha.
Graphs that have a weighted adjacency matrix with spectrum $\{\lambda_1^{n2}, \lambda_2^2\}$.
(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
ErdősKoRado theorem for tcycleintersecting 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 setpartition 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.
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 ErdősKoRado Theorem for Intersecting Families of Permutations.
Alison's Thesis
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
hillclimbing 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)
 "SetPartitions and Association Schemes"
( PDF)
Presentations for Discrete Math Day and Ottawa Graph Theory Conference
 "Applications of Graph Theory to Covering Arrays"
( PDF)
 "A MulitPartite ErdősKoRado Theorem"
( PDF)
[back to home page]
Last modified: Mon Sep 9 14:55:10 EDT