Hamilton Cycles and Degree Sequences

The connection between the degree-sequence and the hamiltonicity of a graph is a classic and much investigated problem of graph-theory. The weaker and weaker sufficient degree conditions for hamiltonicity of Dirac, Posa, Bondy and Chvatal often belong to the curriculum of introductory graph-theory courses. In this paper we are going to present further degree-sequences that guarantee a Hamilton cycle, which are not included in the above mentioned theorems.