Two small 6-chromatic unit-distance graphs in R~3

摘要

We present 48-vertex and 47-vertex 6-chromatic unit-distance graphs (UDGs) in R~3, improving the previous record of 56 vertices. We speculate that the simplicity and, perhaps more important, modularity of the 47-vertex graph may offer a new and promising basis to search for a 7-chromatic UDG in R~3.