König边着色定理的逻辑强度
The logical strength of König's edge coloring theorem
摘要：
柯尼希的边染色定理说，一个最大度为$n$的二部图的边染色不超过$n$的颜色。我们探讨了这个定理的可计算性理论和逆向数学方面。度由$n$限定的可计算二部图有$n+1$色的可计算边染色，但存在$n$色的边染色的定理等价于RCAo上的WKLo.这就进一步证明了Hirst的一个定理：WKLo在RCAo上等价于所有可数二部$n$ -正则图是$n$完全匹配的并的原理.我们描述了与Vizing边着色定理和Birkhoff定理的可数形式有关的公开问题。
英文摘要：
König's edge coloring theorem says that a bipartite graph with maximal degree $n$ has an edge coloring with no more than $n$ colors. We explore the computability theory and Reverse Mathematics aspects of this theorem. Computable bipartite graphs with degree bounded by $n$ have computable edge colorings with $n+1$ colors, but the theorem that there is an edge coloring with $n$ colors is equivalent to WKLo over RCAo. This gives an additional proof of a theorem of Hirst: WKLo is equivalent over RCAo to the principle that every countable bipartite $n$-regular graph is the union of $n$ complete matchings. We describe open questions related to Vizing's edge coloring theorem and a countable form of Birkhoff's theorem.
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