Alp Muyesser

Hamiltonicity of mildly pseudorandom regular graphs

We show that if an $(n,d,\lambda)$-graph satisfies $\lambda\leq (1-\delta)d$ and $d\gg \delta^{-6}(\log n)^{3}$ for some $\delta>0$, then it is Hamiltonian. A qualitatively similar result was recently proven by Brada\v{c} and Janzer. Our proof here is shorter and gives better quantitative bounds. \par In our proof, as...