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arXiv · 2010.14158

Path decompositions of tournaments

António Girão·Bertille Granet·Daniela Kühn·Allan Lo·Deryk Osthus
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Abstract

In 1976, Alspach, Mason, and Pullman conjectured that any tournament $T$ of even order can be decomposed into exactly ${\rm ex}(T)$ paths, where ${\rm ex}(T):= \frac{1}{2}\sum_{v\in V(T)}|d_T^+(v)-d_T^-(v)|$. We prove this conjecture for all sufficiently large tournaments. We also prove an asymptotically optimal result for tournaments of odd order.

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António Girão, Bertille Granet, Daniela Kühn, Allan Lo, Deryk Osthus. 2022-07-28. Path decompositions of tournaments. https://doi.org/10.1112/plms.12480

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