Alp Muyesser

Hamiltonicity in mildly pseudorandom graphs

Having a (fractional) perfect matching and being connected are two trivial necessary conditions if a graph is to contain a Hamilton cycle, and by no means are they sufficient. Yet, a curious theme in extremal graph theory is that any "non-trivial" conditions that imply the existence of a perfect matching and connectivity also seem to imply the existence of a Hamilton cycle. In this talk, we'll explore this subject through the lens of pseudorandomness.