Vertices of Small Degree in Uniquely Hamiltonian Graphs

LetGbe a uniquely hamiltonian graph onnvertices. We show thatGhas a vertex of degree at mostc log28n+3, wherec=(2−log2 3)−1≈2.41. We show further thatGhas at least two vertices of degree less than four if it is planar and at least four vertices of degree two if it is bipartite.