Dirac subgraphs of powers of cycles are Hamiltonian

Abstract

We show that, for every $\epsilon >0$ and all sufficiently large $k$, any spanning subgraph of the $k$th power of a cycle with minimum degree at least $(1+\epsilon )k$ contains a Hamilton cycle. This asymptotically settles a conjecture of Espuny Díaz, Lichev, and Wesolek.

32 pages