Geodesic
Minimum degree conditions for powers of cycles and paths
Eng Keat Hng1 ; Eng Keat Hng
1Department of Mathematics, London School of Economics and Political Science, London, United Kingdom
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 795-800 
Eng Keat Hng; Eng Keat Hng. Minimum degree conditions for powers of cycles and paths. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 795-800. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a67/
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     author = {Eng Keat Hng and Eng Keat Hng},
     title = { Minimum degree conditions for powers of cycles and paths},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {795--800},
     year = {2019},
     volume = {88},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a67/}
}
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Voir la notice de l'article provenant de la source Comenius University

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 kth 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 kth 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.