# Embedding spanning subgraphs in uniformly dense and inseparable graphs

28 Sep 2019 Ebsen Oliver Maesaka Giulia S. Reiher Christian Schacht Mathias Schülke Bjarne

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 Koml\'os, Sark\"ozy, and Szemer\'edi resolved the conjectures of P\'osa and Seymour and obtained optimal minimum degree conditions for this problem by showing that $\mu=\frac{k}{k+1}$ suffices for large $n$... (read more)

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