A Study on the Degree-Based Conditions for Hamilton Properties

In this talk, we will survey some well-known theorems regarding graphs being Hamiltonian or with stronger Hamiltonianrties. Recently, it has been found that most graphs satisfying the conditions in these theorems are indeed with the same hamiltonian properties even when some faults occur. Namely, except for certain cases, these theorems imply graphs with fault-tolerant hamiltonian, hamiltonian connected, or r*-connected accordingly. Graph terminologies will be introduced, and audiences without any background are welcome.