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  "body": "\n## Definition\n\nLet $G$ be a [[graph|0JD5C82QMB]].\nA cycle in $G$ is a [[circuit|0PD57PSHNR]] $(w_0, w_1, \\dots, w_k)$ whose vertices $w_1, \\dots, w_k$ are pairwise distinct.\n\n## Remarks\n\nThe only repeated vertex is $w_0 = w_k$. In a simple graph, each cycle has length $k \\ge 3$.\nThe vertices and edges of a cycle of length $k$ form a subgraph isomorphic to the [[cycle graph|0QQ0F12962]] $C_k$.\nA graph with no cycle is [[acyclic|0XNN9Z8E5A]].\n\n## Explanations\n\n### L1 human\n\nA cycle is a round trip that visits each of its vertices once and comes back to the start.\nA triangle is the shortest possible cycle in a simple graph.\n",
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