The National Science Foundation, Combinatorics Program of the Division of Mathematical Sciences, has awarded funding to Augusta University’s Dr. Guangming Jing for his research proposal, “Density and Edge Coloring.”
The total intended award amount is $94,005, running from April 1, 2020, to March 31, 2023. In the first two years, Jing, an assistant professor in the College of Science and Mathematics, will receive $62,670; however, the amount may differ based on performance in the last year. This grant contributes greatly to the Department of Mathematics’ goal of becoming a department recognized for its research.
“We in the department are all very proud of Dr. Jing. The awarding of this grant is very impressive,” said Dr. Bruce Landman, chair and professor of the Mathematics Department. “NSF funding for research grants in pure mathematics is quite competitive. The fact that this is Guangming’s first year after obtaining his PhD, and that he is the only name on this grant, makes this award truly special.”
Prior to receiving the grant, Jing had already published two journal articles on edge coloring in 2019.
“Through a conjecture (a mathematical hypothesis) that we have recently proved, the difficulty of edge coloring is very related to the density of the edges of the graph,” he said. “The original proof itself is over 100 pages, and we reduced the length a little bit over last year.”
Jing works with the techniques developed from Goldberg-Seymour Conjecture to solve density-related problems. While calculating the density is easy, finding an optimum coloring of a graph is not. Several density-related conjectures will help to connect the density with the difficulty of coloring the graph. The higher the density, the more colors are needed. For some problems, even though mathematicians know exactly the minimum number of colors to use, they do not yet have fast algorithms to find the actual coloring.
“I have listed four questions that could be attacked through the newly developed density-related techniques in the abstract. For the last problem, I’m planning to find fast coloring algorithms because proving something is one thing, but determining a way to create related applicable algorithms is also important,” he said.
Read his abstract here.
Originally from Shandong, China, Jing obtained his undergraduate degree in Nanjing and his master’s degree in Taiyuan; both degrees are in mathematics. Jing came to Augusta University in fall 2019 after earning his PhD in mathematics and statistics from Georgia State University in spring 2019.
“When I moved from China to attend GSU, I really learned to like Georgia. That’s one reason that I stayed. Augusta University has become bigger, so I believe it’s better to join the growth,” he said.