A [k, k+1]-Factor Containing A Given Hamiltonian Cycle

We prove the following best possible result. Let k 2 be an integer and G be a graph of order n with minimum degree at least k. Assume n 8k - 16 for even n and n 6k-13 for odd n. If the degree sum of each pair of nonadjacent vertices of G is at least n, then for any given Hamiltonian cycle C of G, G has a [k, k + 1]-factor containing C. Submitted: December 15, 1997; Accepted: November 27, 1998. MR Subject Number: 05C75

• Type: Journal
• Year: 1999
• Where: COMBINATORICS
• Authors: Mao-cheng Cai, Yanjun Li, Mikio Kano
• Keywords: COMBINATORICS 1999, Degree Sum, Minimum Degree, Nonadjacent Vertices