r/ErdosTasks

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#19Chromatic number of K_n decompositions$500
OPENHARDgraph theorychromatic number
If $G$ is an edge-disjoint union of $n$ copies of $K_n$ then is $\chi(G)=n$?
Notes: Kahn proved chi(G) <= (1+o(1))n. Kang, Kelly, Kuhn, Methuku, and Osthus proved it for all sufficiently large n. The problem remains open for small n.
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