%A Ebsen, Oliver
%A Maesaka, Giulia Satiko
%A Reiher, Christian
%A Schacht, Mathias
%A Schülke, Bjarne
%D 2019
%T Powers of Hamiltonian cycles in mu-inseparable graphs
%K
%X We consider sufficient conditions for the existence of k-th powers of Hamiltonian cycles in n-vertex graphs G with minimum degree mu*n for arbitrarily small mu>0. About 20 years ago Komlós, Sárközy, and Szemerédi resolved the conjectures of Pósa and Seymour and obtained optimal minimum degree conditions for this problem by showing that mu=k/(k+1) suffices for large n. Consequently, for smaller values of mu the given graph G must satisfy additional assumptions. We show that inducing subgraphs of density d>0 on linear subsets of vertices and being inseparable, in the sense that every cut has density at least mu>0, are sufficient assumptions for this problem. This generalises a recent result of Staden and Treglown.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1295
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 637-641%V 88
%N 3
%@ 0862-9544
%8 2019-07-29