A Study on the Degree-Based Conditions for Hamiltonian Properties
Shin-Shin Kao
University of Southern California
In this talk, we will survey some well-known theorems regarding graphs being hamiltonian or with stronger hamiltonian properties. Recently, it is 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.
