Minimum degrees for powers of paths and cycles
Abstract
We study minimum degree conditions under which a graph G contains kth powers of paths and cycles of arbitrary specified lengths. We determine precise thresholds, assuming that the order of G 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.
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