# Sh:923

- Ardal, H., Maňuch, J., Rosenfeld, M., Shelah, S., & Stacho, L. (2009).
*The odd-distance plane graph*. Discrete Comput. Geom.,**42**(2), 132–141. DOI: 10.1007/s00454-009-9190-2 MR: 2519871 -
Abstract:

The vertices of the odd-distance graph are the points of the plane \mathbb{R}^2. Two points are connected by an edge if their Euclidean distance is an odd integer. We prove that the chormatic number of this graph is at least five. We also prove that the odd-distance graph in \mathbb{R}^2 is countably choosable, which such a graph in \mathbb{R}^3 is not. - published version (10p)

Bib entry

@article{Sh:923, author = {Ardal, Hayri and Ma{\v{n}}uch, J{\'a}n and Rosenfeld, Moshe and Shelah, Saharon and Stacho, Ladislav}, title = {{The odd-distance plane graph}}, journal = {Discrete Comput. Geom.}, fjournal = {Discrete \& Computational Geometry. An International Journal of Mathematics and Computer Science}, volume = {42}, number = {2}, year = {2009}, pages = {132--141}, issn = {0179-5376}, mrnumber = {2519871}, mrclass = {05C10 (05C12)}, doi = {10.1007/s00454-009-9190-2} }