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K\"onig's edge coloring theorem says that a bipartite graph with maximaldegree $n$ has an edge coloring with no more than $n$ colors. We explore thecomputability theory and Reverse Mathematics aspects of this theorem.Computable bipartite graphs with degree bounded by $n$ have computable edgecolorings with $n+1$ colors, but the theorem that there is an edge coloringwith $n$ colors is equivalent to WKLo over RCAo. This gives an additional proofof a theorem of Hirst: WKLo is equivalent over RCAo to the principle that everycountable bipartite $n$-regular graph is the union of $n$ complete matchings.We describe open questions related to Vizing's edge coloring theorem and acountable form of Birkhoff's theorem.

The logical strength of K\"onig's edge coloring theorem