Abstract
Let k ≥ 2 be an integer and G a 2-connected graph of order {pipe}G{pipe} ≥ 3 with minimum degree at least k. Suppose that {pipe}G{pipe} ≥ 8k - 16 for even {pipe}G{pipe} and {pipe}G{pipe} ≥ 6k - 13 for odd {pipe}G{pipe}. We prove that G has a [k, k + 1]-factor containing a given Hamiltonian cycle if max{degG(x), degG(y)} ≥ {pipe}G{pipe}/2 for each pair of nonadjacent vertices x and y in G. This is best possible in the sense that there exists a graph having no k-factor containing a given Hamiltonian cycle under the same conditions. The lower bound of {pipe}G{pipe} is also sharp.
Original language | English |
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Pages (from-to) | 273-281 |
Number of pages | 9 |
Journal | Australasian Journal of Combinatorics |
Volume | 26 |
Publication status | Published - 2002 |
Externally published | Yes |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics