Minimum degrees for powers of paths and cycles
arXiv:2005.02210 · doi:10.1137/20M1359183
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, Böttcher and Hladký [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.
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