My research interests lie principally in structural graph theory, though I am also interested in other areas of combinatorics and number theory. At the moment I am interested in what structural information can be obtained about a graph from its degree sequence and/or the subgraphs it does or does not induce. I am particularly interested where the two areas overlap--in graph problems seeking to relate the presence or absence of induced subgraphs in a graph G to conditions on the degree sequence of G. For a more detailed summary of my research, click here (last updated Nov. 2011).

Publications

• Graph classes characterized both by forbidden subgraphs and degree sequences. Joint work with Stephen G. Hartke and Mohit Kumbhat. Journal of Graph Theory, vol. 57 (2008), no. 2, pages 131-148.
• Antimagic labeling and canonical decomposition of graphs. (preprint) Information Processing Letters, vol. 110 (2010), pages 261-263. 
• Degree-associated reconstruction number of graphs. (preprint) Joint work with Douglas B. West. Discrete Mathematics, vol. 310 (2010), no. 20, pages 2600-2612.
• Length thresholds for graphic lists given fixed largest and smallest entries and bounded gaps. (preprint) Joint work with Stephen G. Hartke, Kyle F. Jao, and Douglas B. West. To appear in Discrete Mathematics. doi:10.1016/j.disc.2011.05.001
• The A₄-structure of a graph. (preprint) Joint work with Douglas B. West. To appear in Journal of Graph Theory. doi:10.1002/jgt.20639
• Havel-Hakimi residues of unigraphs. (preprint) Information Processing Letters, vol. 112 (2012), pages 44-48. doi:10.1016/j.ipl.2011.10.011

Preprints

• Non-minimal degree-sequence-forcing triples. Joint work with Stephen G. Hartke and Mohit Kumbhat. Submitted.
• On {2K₂,C₄,chair}-free graphs and related classes. Submitted.
• On 2-switches and isomorphism classes. Submitted.

Theses

• On induced subgraphs, degree sequences, and graph structure. My doctoral dissertation. University of Illinois at Urbana-Champaign, 2009.
• A forbidden subgraph characterization problem and a minimal-element subset of universal graph classes. My master's thesis. Brigham Young University, 2004.

Recent talks

• October 15, 2011, AMS Central Section Meeting (Lincoln, NE). "Residues and independence numbers of unigraphs." Slides (PDF, 270KB)
• April 8, 2011, MAA Rocky Mountain Section Meeting (Boulder, CO). "Residues and independence numbers of unigraphs."
• August 7, 2010, MathFest 2010 (Pittsburgh, PA). "On antimagic labelings of graphs."
• June 16, 2010, SIAM Conference on Discrete Mathematics (Austin, TX). "Degree sequences, vertex substitutions, and matrogenic graphs."  Slides (PDF, 246KB).
• April 17, 2010, MAA Rocky Mountain Section Meeting (Fort Collins, CO). "Degree sequences, vertex substitutions, and matrogenic graphs."
• March 9, 2010, Discrete Math Seminar, University of Nebraska-Lincoln (Lincoln, NE). "Substitution closures of the split graphs and matrogenic graphs."
• February 16-17, 2010, math. dept. colloquiums at Black Hills State University (Spearfish, SD) and South Dakota School of Mines and Technology (Rapid City, SD). "Degree-sequence-forcing sets: when hasty generalizations are okay." Slides (PDF, 670KB).