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arXiv · 1907.08479

An approximate version of Jackson's conjecture

Anita Liebenau·Yanitsa Pehova
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Abstract

In 1981 Jackson showed that the diregular bipartite tournament (a complete bipartite graph whose edges are oriented so that every vertex has the same in- and outdegree) contains a Hamilton cycle, and conjectured that in fact the edge set of it can be partitioned into Hamilton cycles. We prove an approximate version of this conjecture: For every $c>1/2$ and $\varepsilon>0$ there exists $n_0$ such that every $cn$-regular bipartite digraph on $2n\geq n_0$ vertices contains $(1-\varepsilon)cn$ edge-disjoint Hamilton cycles.

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Anita Liebenau, Yanitsa Pehova. 2022-09-18. An approximate version of Jackson's conjecture. https://arxiv.org/abs/1907.08479

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