ZHANAR BERIKKYZY, Fairfield University
Authors: G. Araujo-Pardo, Zh. Berikkyzy, J. Faudree, K. Hogenson, R. Kirsch, L. Lesniak, and J. McDonald
2022 AWM Research Symposium
Women from the Graduate Research Workshop in Combinatorics

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.

Back to Search Research Symposium Abstracts