Abstract
We consider the problem of finding long cycles in balanced tripartite graphs. We survey the relevant literature, namely degree and edge conditions for Hamiltonicity and long cycles in graphs, including bipartite and k-partite results where they exist. We 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) ≥ 3n 2 − 4n + 5 and n ≥ 14.
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Acknowledgements
The work described in this article is a result of a collaboration made possible by the IMA’s Workshop for Women in Graph Theory and Applications. Research of the fifth author was supported in part by NSF grant DMS-1839918.
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Araujo-Pardo, G. et al. (2021). Finding Long Cycles in Balanced Tripartite Graphs: A First Step. In: Ferrero, D., Hogben, L., Kingan, S.R., Matthews, G.L. (eds) Research Trends in Graph Theory and Applications. Association for Women in Mathematics Series, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-030-77983-2_1
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