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  "body": "\n## Summary\n\nThe girth of a graph is the length of its shortest [[cycle|0Z05VCBQ7Y]], and it is infinite for a graph without cycles.\nLarge girth means that the graph looks like a tree near each vertex.\nGraphs with both large girth and large chromatic number exist, a classical result of the probabilistic method.\nThe node [[girth|WZ4JGTG6ZD]] gives the precise definition.\n\n## Explanations\n\n### L1 human\n\nWalk around the smallest loop you can find in a graph and count its edges: that number is the girth.\nA triangle gives girth $3$, and a graph whose smallest loops are squares has girth $4$, like a grid of streets.\nThe [[Petersen graph|0NR95CTFCZ]] has girth $5$: it has pentagons but no triangles and no squares.\n",
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