Mary Radcliffe

Office: 6436 AP&M
E-mail: mradcliffe@math.ucsd.edu

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Research Statement

Teaching Statement

Research:

I am currently a fifth year graduate student in the Department of Mathematics at the University of California, San Diego. My advisor is Fan Chung Graham. My research interests include random graphs and spectral graph theory, and more generally, probabilistic combinatorics. I am especially interested in ways to use random matrices to provide information about corresponding random graphs. More information about my research interests and publications can be found on my research page and CV.

Teaching:

I also greatly enjoy teaching mathematics. I have worked as a teaching assistant and as a course instructor of record at both UCSD and Western Michigan University. To see more about my teaching experience and what my students have to say about me, please visit my teaching page.


Papers:

  1. Connectivity of Stochastic Kronecker Graphs (with S. Young). In preparation.
    We provide a characterization of connectivity for Stochastic Kronecker Graphs with an arbitrarily sized generating matrix.
  2. On the spectra of Multiplicative Attribute Graphs (with S. Young). In preparation.
    We consider Stochastic Kronecker Graphs, and, more generally, Multiplicative Attribute Graphs. We provide estimates for the eigenvalues of the normalized Laplacian matrix for these graphs, as well as for the adjacency matrix for Stochastic Kronecker Graphs.
  3. On the spectra of general random graphs (with F. Chung) Electronic Journal of Combinatorics 18(1) (2011), P215.
    Given an edge-independent random graph, we prove that the spectra of the adjacency matrix and normalized Laplacian matrix are concentrated on the spectra of the adjacency matrix and the Laplacian corresponding to the expected graph, respectively. The only requirement on the graph is a minor density condition.
  4. Giant components in Kronecker graphs (with P. Horn) To appear in Random Structures and Algorithms
    We provide a necessary and sufficient condition for a Stochastic Kronecker Graph to have a giant component. Moreover, we establish the asymptotic size of the giant component in this graph.
  5. Irregular colorings of graphs (with P. Zhang) Bulletin of the Institute of Combinatorics and its Applications. 49 (2007) 41-59.
    We define the irregular chromatic number, and investigate this parameter for cycles. Moreover, we characterize graphs with irregular chromatic number n and construct graphs with arbitrarily large irregular chromatic number and arbitrarily small chromatic number.
  6. On irregular colorings of graphs (with P. Zhang) AKCE International Journal of Graphs and Combinatorics. 3 (2006) 175-191.
    We examine the irregular chromatic number for disconnected graphs, and establish sharp Nordhaus-Gaddum inequalities for the irregular chromatic number.
  7. On the irregular chromatic number of a graph (with F. Okamoto and P. Zhang) Congressus Numerantium. 181 (2006) 129-150.
    We discuss the irregular chromatic number of trees, and investigate the effects of minor changes to a graph, such as vertex or edge addition or deletion, on the irregular chromatic number.




Last updated: 16 October 2011.