Fan Chung Graham

Summary: Fan Chung, a role model to mathematics students, has done key work in Ramsey theory.

Known professionally as Fan Chung, Fan R. K. Chung Graham (1949–) is a Taiwanese-American mathematician specializing in combinatorics. She earned her doctorate from the University of Pennsylvania in 1974, where she was a student of Herbert Wilf (1931–), then spent two decades at Bell Labs and Bell Corp. In 1983, she married Ron Graham, a famous mathematician in his own right; she has two children from a previous marriage. In 1994, she left industry and returned to academia as an endowed professor at the University of Pennsylvania. Three years later she accepted her current position as a professor at the University of California, San Diego.

Fan Chung loved mathematics from a young age in Taiwan and decided in high school to be a mathematician. She gravitated to combinatorics because the problems were fun and “many problems… were easily explained, you could get into them quickly, but getting out was often very hard.” She is a role model to mathematics students, especially young women entering mathematics. Fan Chung advises students, “Don’t be intimidated!” and emphasizes the importance of seeking and exploring the connections between different topics in mathematics and applications. “It is like playing a game of Go.… If your territory is all connected together, then each piece is strong and useful.”

Another theme in Fan Chung’s discussions about mathematics is the importance of communication. “As an undergraduate in Taiwan, I was surrounded by good friends and many women mathematicians. We enjoyed talking about mathematics and helping each other.” At Bell Labs, she was intimidated at first by some of the research mathematicians and scientists with whom she worked. However, her interest in diverse mathematical problems led her to inquire about others’ work. Then, as she said, “You make mathematical friends and share the fun!”

Fan Chung’s primary research interests are in random graphs, spectral graph theory, and extremal graph theory. She has also made many contributions in discrete geometry, communication networks, and algorithms. Her generalization of the Erdos–Rényi model for random graphs has applications to the study of large information networks. At the same time, she has blended and balanced her work and family lives. When she became pregnant with her second child, she reassured others, “Since I already had one at home, I thought what’s the problem with one more?… I just took four weeks vacation and wrote one paper in between.” She has also said that it is “quite wonderful” to have a supportive spouse with whom she can share her ideas and challenges. Recreationally she paints, including portraits of mathematicians she has known. In 1999, the Graham home, which has a unique circular design, was named “Home of the Year” by Décor & Style magazine and was also featured on the television program “Extreme Homes.”

Ramsey Theory

Fan Chung’s doctoral dissertation and much of her work since come under the general heading of Ramsey theory, named for British mathematician and economist Frank Ramsey (1903–1930). This branch of combinatorial mathematics deals with the inevitability of certain types of order and patterns. The simplest nontrivial result says that, in any group of six people, there are either three where all know each other or three where none know each other. If there are six vertices with a line connecting each pair, and each line is colored either red or blue, there will necessarily be either a red triangle or a blue triangle. A fundamental result of the theory says if there are n vertices, with each pair connected by a line, and if each line is colored in any of k colors, then there will be some n vertices that are all connected in the same color, provided n is large enough in terms of n and k. It is very difficult to estimate well how large n must be, given values of n and k. Ramsey theory is not limited to people. The objects of study may be, for instance, stars or sequences of random numbers. There are also connections to number theory and implications in scheduling problems.

Bibliography

Albers, Don. “Making Connections: A Profile of Fan Chung.” Math Horizons (September 1994).

Chung, Fan. Spectral Graph Theory. Providence, RI: AMS, 1997.

Chung, Fan, and Ronald Graham. Erdos on Graphs: His Legacy of Unsolved Problems. Wellesley, MA: A K Peters, 1998.

Graham, Ronald, Bruce Rothschild, and Joel Spencer. Ramsey Theory. Hoboken, NJ: Wiley, 1990.