Abstract
The paper deals with estimating the r-colorability threshold for a random k-uniform hypergraph in the binomial model H(n,k,p). We consider the sparse case, when the expected number of edges is a linear function of n, pnk=cn, and c>0, k⩾4, r⩾3 are some fixed constants. We show that if c<rk−1lnr−12lnr−r−1r+O(k2r1−k∕3lnr) then H(n,k,cn∕nk) is r-colorable with probability tending to 1 as n→∞.
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