On the Chromatic Number of the Euclidean Plane

@inproceedings{Moorhousey1999OnTC,
  title={On the Chromatic Number of the Euclidean Plane},
  author={G. Eric Moorhousey},
  year={1999}
}
  • G. Eric Moorhousey
  • Published 1999
Deene two points of the Euclidean plane R 2 to be adjacent if they are at distance 1 from each other. It is known that the chromatic number of the resulting graph satisses 4 (R 2) 7. We obtain some partial results concerning (K 2) for subbelds K R. We believe that these results may help to focus the problem of determining (R 2)| either by providing a new upper bound, or by showing where to look for a new subgraph which increases the lower bound. 1. A Field-Theoretic Approach to the Problem Let… CONTINUE READING

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