Hypergraph coloring up to condensation

Peter Ayre; Amin Coja-Oghlan; Catherine Greenhill

Hypergraph coloring up to condensation

Discrete Mathematics 2018-04-16 v4 Combinatorics

Authors: Peter Ayre , Amin Coja-Oghlan , Catherine Greenhill

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].

Keywords

graph coloring

Cite

@article{arxiv.1508.01841,
  title  = {Hypergraph coloring up to condensation},
  author = {Peter Ayre and Amin Coja-Oghlan and Catherine Greenhill},
  journal= {arXiv preprint arXiv:1508.01841},
  year   = {2018}
}

Comments

31 pages. Revised version, addressing referees' comments

Hypergraph coloring up to condensation

Abstract

Keywords

Cite

Comments

Related papers