Several New Results On Hamiltonicity Of Graphs

In this thesis, the author presented a new sufficient condition on s-traceability of graphs concerning the neighborhood intersections of the independent sets in partially square graphs. This sufficient condition was deduced by employing the technique of vertex insertion and the conception of LTW-sequence. Furthermore, four new sufficient conditions on hamiltonian and almost-hamiltonian graphs also were proved with the vertex insertion technique. The result generalizes Ore's theorem.