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Papers
Papers
On graphs with chromatic number and maximum degree both equal to 9
On graphs with chromatic number and maximum degree both equal to 9
A joint work with Dr. Jessica McDonald
ArXiv: https://arxiv.org/abs/2408.12693
Abstract: An equivalent version of the Borodin-Kostochka Conjecture, due to Cranston and Rabern, says that any graph with χ=Δ=9 contains K₃ ∨ E₆ as a subgraph. Here we prove several results in support of this conjecture, where vertex-criticality and forbidden substructure conditions get us either close or all the way to containing K₃ ∨ E₆.
A decomposition of a complete graph with a hole
A decomposition of a complete graph with a hole
A joint work with Dr. Roxanne Back, Alejandra Brewer-Castano, and Jessica Finocchiaro
https://www.scirp.org/journal/paperinformation?paperid=106325
Abstract: In the field of design theory, the most well-known design is a Steiner Triple System. In general, a G-design on H is an edge-disjoint decomposition of H into isomorphic copies of G. In a Steiner Triple system, a complete graph is decomposed into triangles. In this paper we let H be a complete graph with a hole and G be a complete graph on four vertices minus one edge, also referred to as a K₄ - e. A complete graph with a hole, Kd + v, consists of a complete graph on d vertices, Kd, and a set of independent vertices V of size v, where each vertex in V is adjacent to each vertex in Kd. When d is even, we give two constructions for the decomposition of a complete graph with a hole into copies of K₄ - e: the Alpha-Delta Construction, and the Alpha-Beta-Delta Construction. By restricting d and v so that v= 2(d-1) -5a, we are able to resolve both of these cases for a subset of Kd + v using difference methods and 1-factors.
Presentations
Presentations
TBD. Special session on graphs, hypergraphs, and extremal combinatorics at Joint Mathematics Meetings, Seattle, Washington, January 2025.
Results pertaining to the Borodin Kostochka Conjecture. Auburn Combinatorics Seminar, Auburn University, October 2024.
On graphs with chromatic number and maximum degree both equal to nine. McNeese Math Seminar, McNeese State University, October 2024.
On graphs with chromatic number and maximum degree both equal to nine. Auburn Math Graduate Student Seminar, Auburn University, October 2024.
On graphs with chromatic number and maximum degree both equal to nine. Session for colorings on graphs at Virtual Conference for Women in Combinatorics. July 2024.
Mozhan Partitions. Auburn Math REU Seminar, Auburn University, June 2023.
From partitioning to degeneracy to coloring. Auburn Math Student Research Seminar, Auburn University, September 2022.
Decomposition of a complete graph using K4 – e. Florida Gulf Coast University’s Aspire Conference, Florida Gulf Coast University, January 2020.
Bilingualism in conjunction with math learning and the implications for public school teachers. Florida Southern College Math Thesis Committee, Florida Southern College, November 2019.
Contact Info
Contact Info
Email: rcg0036@auburn.edu
Office: 118E Parker Hall
Mailing Address:
Department of Mathematics and Statistics
221 Parker Hall
Auburn University, AL 36849
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