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  "body": "\n## Statement\n\nIn the mathematics of [[graph coloring|0NCPXH194Y]], **Cereceda’s conjecture** is an unsolved problem on the distance between pairs of colorings of sparse graphs. It states that, for two different colorings of a graph of degeneracy $d$, both using at most $d + 2$ colors, it should be possible to reconfigure one coloring into the other by changing the color of one vertex at a time, using a number of steps that is quadratic in the size of the graph. The conjecture is named after Luis Cereceda, who formulated it in his 2007 doctoral dissertation.\n",
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