Bauer, D., Broersma, H. J., van den Heuvel, Jan 
ORCID: 0000-0003-0897-9148, Kahl, N. and Schmeichel, E.
(2012)
Degree sequences and the existence of k-Factors.
Graphs and Combinatorics, 28 (2).
pp. 149-166.
ISSN 0911-0119
Abstract
We consider sufficient conditions for a degree sequence π to be forcibly k-factor graphical. We note that previous work on degrees and factors has focused primarily on finding conditions for a degree sequence to be potentially k-factor graphical. We first give a theorem for π to be forcibly 1-factor graphical and, more generally, forcibly graphical with deficiency at most β ≥ 0. These theorems are equal in strength to Chvátal's well-known hamiltonian theorem, i. e., the best monotone degree condition for hamiltonicity. We then give an equally strong theorem for π to be forcibly 2-factor graphical. Unfortunately, the number of nonredundant conditions that must be checked increases significantly in moving from k = 1 to k = 2, and we conjecture that the number of nonredundant conditions in a best monotone theorem for a k-factor will increase superpolynomially in k. This suggests the desirability of finding a theorem for π to be forcibly k-factor graphical whose algorithmic complexity grows more slowly. In the final section, we present such a theorem for any k ≥ 2, based on Tutte's well-known factor theorem. While this theorem is not best monotone, we show that it is nevertheless tight in a precise way, and give examples illustrating this tightness.
| Item Type: | Article |
|---|---|
| Official URL: | http://www.springer.com/new+%26+forthcoming+titles... |
| Additional Information: | © 2012 Springer |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 03 Apr 2012 15:42 |
| Last Modified: | 12 Dec 2024 00:07 |
| URI: | http://eprints.lse.ac.uk/id/eprint/42951 |
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