On the Extremal Number of Edges in 2-Factor Hamiltonian Graphs.

In this paper we consider the question of determining the maximum number of edges in a Hamiltonian graph of order n that contains no 2-factor with more than one cycle, that is, 2-factor Hamiltonian graphs. We obtain exact results for both bipartite graphs, and general graphs, and construct extremal graphs in each case. [ABSTRACT FROM AUTHOR]