Hamilton decompositions of regular tripartite tournaments- a partial resolution

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• Joanna Lada (LSE)
• Thursday 23 November 2023, 15:00-16:00
• Poynting Small Lecture Theatre (S06).

If you have a question about this talk, please contact Dr. Jan Kurkofka.

Given a Hamiltonian graph $G$, it is natural to ask whether it admits a full Hamilton decomposition. In the setting of regular oriented graphs, this has been confirmed for sufficiently large regular tournaments (Kühn, Osthus (2013)), bipartite tournaments (Granet (2022)), and $k$-partite tournaments when $k\geq 4$ (Kühn, Osthus (2013)).

For tripartite tournaments, a complete decomposition is not always possible; the known counterexample, $\mathcal{T}(\Delta)$, consisting of the blowup of $C_3$ with a single triangle reversed. However, it is reasonable to suggest that all such non-decomposable regular tripartite tournaments fall within a specifiable class, and perhaps are even are all isomorphic to $\mathcal{T}(\Delta)$.

In this talk we give a partial resolution towards this problem. We show that regular tripartite tournaments fall within one of three structural families. We prove Hamilton decomposability of two of these, and indicate a general strategy towards approaching the third.

Joint work with Francesco Di Braccio, Viresh Patel, Yanitsa Pehova, and Jozef Skokan.

This talk is part of the Combinatorics and Probability seminar series.

This talk is included in these lists:

• Combinatorics and Probability seminar
• Poynting Small Lecture Theatre (S06)
• School of Mathematics events

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