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 |
|---|---|
| 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
Cite this
Degree conditions for the existence of [k, k + 1]-factors containing a given Hamiltonian cycle. / Matsuda, Haruhide.
In: Australasian Journal of Combinatorics, Vol. 26, 2002, p. 273-281.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Degree conditions for the existence of [k, k + 1]-factors containing a given Hamiltonian cycle
AU - Matsuda, Haruhide
PY - 2002
Y1 - 2002
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=1642389779&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:1642389779
VL - 26
SP - 273
EP - 281
JO - Australasian Journal of Combinatorics
JF - Australasian Journal of Combinatorics
SN - 1034-4942
ER -