Algebra and Combinatorics Seminar

Date: December 3, 2021

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Zhanar Berikkyzy, Fairfield University

Title: Long cycles in Balanced Tripartite Graphs

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 $k$-partite results. We will then prove that if $G$ is a balanced tripartite graph on $3n$ vertices, $G$ must contain a cycle of length at least $3n-1$, provided that $e(G) \geq 3n^2-4n+5$ and $n\geq 14$. 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.