Abstract
We prove that for every m∈N and every δ∈(−m,0), the chromatic number of the preferential attachment graph PAt(m,δ) is asymptotically almost surely equal to m+1. The proof relies on a combinatorial construction of a family of digraphs of chromatic number m+1 followed by a proof that asymptotically almost surely there is a digraph in this family, which is realised as a subgraph of the preferential attachment graph.
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