Almost every C6-free graph is the disjoint union of a stable set and the complement of a graph of girth 5; analogues for C8, C10, and longer even cycles complete the induced-cycle typical-structure picture.
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The Global Structure of a Typical Graph Without $H$ as an Induced Subgraph when $H$ is a Cycle
Almost every C6-free graph is the disjoint union of a stable set and the complement of a graph of girth 5; analogues for C8, C10, and longer even cycles complete the induced-cycle typical-structure picture.