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Even circuit theorem : ウィキペディア英語版 | Even circuit theorem In extremal graph theory, the even circuit theorem is a result of Paul Erdős according to which an -vertex graph that does not have a simple cycle of length can only have edges. For instance, 4-cycle-free graphs have edges, 6-cycle-free graphs have edges, etc. ==History== The result was stated without proof by Erdős in 1964.〔.〕 published the first proof, and strengthened the theorem to show that, for -vertex graphs with edges, all even cycle lengths between and occur.〔.〕
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