%A Hng, Eng Keat
%D 2019
%T Minimum degree conditions for powers of cycles and paths
%K
%X The study of conditions on vertex degrees in a host graph G for the appearance of a target graph H is a major theme in extremal graph theory. The k th power of a graph F is obtained from F by joining any two vertices at distance at most k. We study minimum degree conditions under which a graph G contains the k th power of cycles and paths of arbitrary specified lengths. We determine precise thresholds, assuming that the order of G is large. This extends a result of Allen, Böttcher and Hladký concerning the containment of squared paths and squared cycles of arbitrary specified lengths and settles a conjecture of theirs in the affirmative.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1274
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 795-800%V 88
%N 3
%@ 0862-9544
%8 2019-07-30