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arXiv · 1508.01841

Hypergraph coloring up to condensation

Peter Ayre·Amin Coja-Oghlan·Catherine Greenhill
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Abstract

Improving a result of Dyer, Frieze and Greenhill [Journal of Combinatorial Theory, Series B, 2015], we determine the $q$-colorability threshold in random $k$-uniform hypergraphs up to an additive error of $\ln 2+\varepsilon_q$, where $\lim_{q\to\infty}\varepsilon_q=0$. The new lower bound on the threshold matches the "condensation phase transition" predicted by statistical physics considerations [Krzakala et al., PNAS 2007].

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Peter Ayre, Amin Coja-Oghlan, Catherine Greenhill. 2015-08-07. Hypergraph coloring up to condensation. https://arxiv.org/abs/1508.01841

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