Speaker: Zhanar Berikkyzy (Fairfield University)
Abstract: In this talk, we will survey the relevant literature, namely degree and edge conditions for Hamiltonicity and long cycles in graphs, including bipartite and kk-partite results. We will then prove that if GG is a balanced tripartite graph on 3n3n vertices, GG must contain a cycle of length at least 3n−13n-1, provided that e(G)≥3n2−4n+5e(G) \geq 3n^2-4n+5 and n≥14n\geq 14. The result will be generalized to long cycles for 2-connected graphs when the minimum degree is large enough. Joint work with G. Araujo-Pardo, J. Faudree, K. Hogenson, R. Kirsch, L. Lesniak, and J. McDonald.