On the chromatic number of a random hypergraph

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Abstract

We consider the problem of k-colouring a random r-uniform hypergraph with n vertices and cn edges, where k, r, c remain constant as n. Achlioptas and Naor showed that the chromatic number of a random graph in this setting, the case r=2, must have one of two easily computable values as n. We give a complete generalisation of this result to random uniform hypergraphs.

Keywords

Hypergraph
Colouring
Chromatic number
Uniform hypergraph
Random hypergraph

Cited by (0)

1

Supported by EPSRC Research Grant EP/I012087/1.

2

Partially supported by NSF Grant ccf1013110.

3

Research supported by the Australian Research Council grant DP120100197 and performed during the author's sabbatical at Durham University, UK.