The Parts graphs are a set of unit-distance graphs with chromatic number five derived by Jaan Parts in 2019-2020 (Parts 2020a). They provide some of the smallest known examples that establish the solution to the Hadwiger-Nelson problem (i.e., the chromatic number of the plane) as 5, 6, or 7.
The Parts graphs are summarized in the following table and illustrated above.
| vertex count | edge count | discovery date |
| 553 | 2840 | Jul. 4, 2019 |
| 529 | 2630 | Jul. 4, 2019 |
| 525 | 2605 | Jul. 16, 2019 |
| 510 | 2508 | Aug. 3, 2019 |
| 510 | 2502 | prior to Mar. 7, 2020 |
| 509 | 2442 | prior to Mar. 7, 2020 |
Additional graphs on 16, 31, and 199 nodes are also associated with Parts (2020b). The 31-node graph is a small 6-chromatic graph with exactly two edge lengths (1 and
the golden ratio 
). It can be obtained by combining one copy of the 16-vertex
graph with another obtained by rotating about one of the first copy's vertices. (Note
that note that both the 16- and 31-node graphs are edge-edge and edge-vertex degenerate.)
The Parts graphs are implemented in the Wolfram Language as GraphData["PartsGraph509"] etc.
