University of Birmingham > Talks@bham > Combinatorics and Probability seminar > Hamilton decompositions of regular tripartite tournaments- a partial resolution

Hamilton decompositions of regular tripartite tournaments- a partial resolution

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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.

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