Home

About Me

Teaching

Research

Links

Research

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.

Papers

• Graph classes characterized both by forbidden subgraphs and degree sequences. (Joint work with Stephen Hartke and Mohit Kumbhat.) Journal of Graph Theory, vol. 57, issue 2, pages 131-148.
  Abstract: "Given a set F of graphs, a graph G is F-free if G does not contain any member of F as an induced subgraph. We say that F is a degree-sequence-forcing set if, for each graph G in the class C of F-free graphs, every realization of the degree sequence of G is also in C. We give a complete characterization of the degree-sequence-forcing sets F when F has cardinality at most two."
  
• A forbidden subgraph characterization problem and a minimal-element subset of universal graph classes. 2004.
  Abstract: "The direct sum of a finite number of graph classes H_1, ...,H_k is defined as the set of all graphs formed by taking the union of graphs from each of the H_i. The join of these graph classes is similarly defined as the set of all graphs formed by taking the join of graphs from each of the H_i. In this paper we show that if each H_i has a forbidden subgraph characterization then the direct sum and join of these H_i also have forbidden subgraph characterizations. We provide various results which in many cases allow us to exactly determine the minimal forbidden subgraphs for such characterizations. As we develop these results we are led to study the minimal graphs which are universal over a given list of graphs, or those which contain each graph in the list as an induced subgraph. As a direct application of our results we give an alternate proof of a theorem of Barrett and Loewy concerning a forbidden subgraph characterization problem."
  My master's thesis.

Talks

• October 6, 2007, 45th Midwest Graph Theory Conference, Detroit, MI. "Pseudo-split graphs, a decomposition method, and the chair graph."
• May 12, 2007, 44th Midwest Graph Theory Conference, Dayton, OH. "The degree-associated reconstruction number of a graph." Slides (PDF, 57k).
• March 6, 2007, UIUC Graph Theory and Combinatorics Seminar. "The degree-associated reconstruction number of a graph." Slides (PDF, 81k).
• November 3, 2006, 43rd Midwest Graph Theory Conference, Fort Wayne, IN. "Graph classes characterized both by forbidden subgraphs and degree sequences."
• June 25, 2006, SIAM Conference on Discrete Mathematics, Victoria, BC, Canada. "Graph families characterized by both degree sequences and forbidden subgraphs." Slides (PDF, 54k).
• April 22, 2006, Graduate Student Combinatorics Conference, Madison, WI. "Degree-Sequence-Forcing Sets II." Slides (PDF, 83k).
• February 23, 2006, Illinois State University Discrete Math Seminar. "Degree-Sequence-Forcing Sets." Slides (PDF, 139k).
• September 13, 2005, UIUC Combinatorics Seminar. "Graph classes characterized by both forbidden induced subgraphs and degree sequences."

Last updated January 18, 2008.