Minimum degrees for powers of paths and cycles
Combinatorics
2023-06-05 v2
Abstract
We study minimum degree conditions under which a graph contains th powers of paths and cycles of arbitrary specified lengths. We determine precise thresholds, assuming that the order of is large. This extends a result of Allen, B\"ottcher and Hladk\'y [J. Lond. Math. Soc. (2) 84(2) (2011), 269--302] concerning the containment of squares of paths and squares of cycles of arbitrary specified lengths and settles a conjecture of theirs in the affirmative.
Keywords
Cite
@article{arxiv.2005.02210,
title = {Minimum degrees for powers of paths and cycles},
author = {Eng Keat Hng},
journal= {arXiv preprint arXiv:2005.02210},
year = {2023}
}
Comments
60 pages, 3 figures; suggestions by anonymous referees incorporated; accepted for publication in SIAM Journal on Discrete Mathematics. arXiv admin note: text overlap with arXiv:0906.3299 by other authors