Powers of Hamilton cycles in pseudorandom graphs (Q681592)

In this paper, the authors study the appearance of Hamiltonian cycles in pseudorandom graphs. The work is structured into six sections. In Section 1, pseudorandom graphs are presented, a summary of the authors' results and of other authors' results are mentioned. The authors give some basic definitions, outline their proof strategy, provide the main lemmas and prove the main theorem (Theorem 2) in Section 2. In Section 3 and 4, the authors prove their 3 main lemmas. In Section 5, they present how to modify the proof of Theorem 2 to get Theorem 5 (the authors obtain a count close, which is the expected number of labeled copies of the \(k\)-th power of a Hamiltonian cycle in pseudorandom graphs). In the last section, they make some final remarks and present some open problems.