On degree sums, k-factors, and Hamiltonian cycles in graphs - Hernandez, Alana Margarita R. (Animo Repository, 2002)
This paper is an exposition of the article entitled Degree Sums, k-Factors, and Hamiltonian Cycles by R. J. Faudree and J. van den Heuvel which appeared in the journal Graphs and Combinatorics in 1995.The main result of this paper is the following theorem: Let G be a 2-connected graph on n vertices that contains a k-factor and satisfies a3(G) = (3/2) (n-k). Then either is hamiltonian or k = 2 and G E F6.This paper is a generalization of several well-known results in graph theory. It also shows some of these well-known results.