Even circuit theorem (original) (raw)
In extremal graph theory, the even circuit theorem is a result of Paul Erdős according to which an n-vertex graph that does not have a simple cycle of length 2k can only have O(n1 + 1/k) edges. For instance, 4-cycle-free graphs have O(n3/2) edges, 6-cycle-free graphs have O(n4/3) edges, etc.