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Working in subsystems of second order arithmetic, we formulate several representations for hypergraphs. We then prove the equivalence of various vertex coloring theorems to \({\textsf {WKL}}_0\), \({\textsf {ACA}}_0\), and \({\varPi ^1_1 \text {-}}{\textsf {CA}}_0\).

Reverse mathematics and colorings of hypergraphs