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.
Long cycles in Balanced Tripartite Graphs
ZHANAR BERIKKYZY, Fairfield UniversityAuthors: 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