Darryn Bryant

Biography

Professor Darryn Bryant is interested in a branch of mathematics called combinatorics that studies arrangements, patterns, and combinations of discrete objects. A two-time recipient of an Australian Research Council QEII Fellowship, and recipient of the Hall Medal from the Institute of Combinatorics and its Applications. Professor Bryant has solved several important problems in design theory and graph theory and has supervised several successful research students.

Research Interest

Hamilton cycle decompositions of Cayley graphs and related topics There is an unsolved conjecture that every connected 2k-regular Cayley graph on a finite abelian group has a decomposition into k Hamilton cycles. Cayley graphs are graphs based on groups and students who like group theory or graph theory will enjoy working on this and related problems. PhD Project Masters Project The 2-factorisation problem for complete graphs This project examines the existence of 2-factorisations of complete graphs in which the 2-factors are isomorphic to given 2-regular graphs. Using computers the problem has been completely solved for complete graphs of order less than 20 and several infinite families of results are known. However... PhD Project Masters Project