Hypergraph coloring up to condensation | Zendy

Ayre Peter | Zendy; CojaOghlan Amin | Zendy; Greenhill Catherine | Zendy

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Hypergraph coloring up to condensation

Author(s) -

Ayre Peter,

CojaOghlan Amin,

Greenhill Catherine

Publication year - 2019

Publication title -

random structures and algorithms

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.314

H-Index - 69

eISSN - 1098-2418

pISSN - 1042-9832

DOI - 10.1002/rsa.20824

Subject(s) - hypergraph , combinatorics , condensation , frieze , mathematics , series (stratigraphy) , upper and lower bounds , phase transition , discrete mathematics , physics , quantum mechanics , mathematical analysis , thermodynamics , art history , paleontology , biology , art

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 + ε q , where lim q → ∞ε 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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