Yao Bohao is currently a second year student at the University of Melbourne, majoring in Pure Mathematics. He has a wide range of research interests, specifically in the field of Mathematics, ranging from graph theory to analysis. Bohao’s research experience dates back to his first year, when he dabbled in condensed matter physics and gave a short seminar series on his findings. His other research topics includes mathematical modelling and operations research.
Algorithm for finding Hamiltonian cycle in planar graphs
A Hamiltonian cycle is a cycle that passes through each vertex in a graph exactly once. Finding a Hamiltonian cycle in graphs is considered to be an NP-Complete problem, where a solution is hard to find but easy to check. In 1971, Stephen Cook introduces a problem, asking if every problem whose solution can be verified quickly can also be solved quickly by a computer. This question, known as the P vs NP problem, soon became one of the most important open question in mathematics and computer science. While our algorithm is highly unlikely to run in polynomial time, we aim to provide a foundation and ideas in which future researchers could work on.