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  "body": "\n## Summary\n\nIn graph theory, a $\\boldsymbol{k}$**\\-degenerate graph** is an undirected graph in which every non-empty subgraph has at least one vertex of [[degree|0KS0KRDV4Y]] at most $k$. That is, some vertex in the subgraph touches $k$ or fewer of the subgraph's edges. The **degeneracy** of a graph is the smallest value of $k$ for which it is $k$-degenerate. The degeneracy of a graph is a measure of how sparse it is, and is within a constant factor of other sparsity measures such as the arboricity of a graph.\n",
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