Many Vertex‐Disjoint Even Cycles of Fixed Length in a Graph

ABSTRACT For every integer , we determine the maximum number of edges in an ‐vertex graph with at most vertex‐disjoint copies of when is sufficiently large and lies in the interval , where is a constant depending only on . Moreover, we show that the unique extremal graph is obtained from the complete bipartite graph between of size and of size , by adding all edges within and exactly one additional edge within . The question for and was explored in prior work [25], revealing different extremal structures in these cases. Our result can be viewed as an extension of the theorems by Egawa and Verstraëte, where the focus was on the existence of many vertex‐disjoint cycles of the same length without any length constraints.