TY - JOUR
T1 - The odd-distance plane graph
AU - Ardal, Hayri
AU - Maňuch, Ján
AU - Rosenfeld, Moshe
AU - Shelah, Saharon
AU - Stacho, Ladislav
PY - 2009/9
Y1 - 2009/9
N2 - The vertices of the odd-distance graph are the points of the plane ℝ2. Two points are connected by an edge if their Euclidean distance is an odd integer. We prove that the chromatic number of this graph is at least five. We also prove that the odd-distance graph in ℝ2 is countably choosable, while such a graph in ℝ3 is not.
AB - The vertices of the odd-distance graph are the points of the plane ℝ2. Two points are connected by an edge if their Euclidean distance is an odd integer. We prove that the chromatic number of this graph is at least five. We also prove that the odd-distance graph in ℝ2 is countably choosable, while such a graph in ℝ3 is not.
KW - Graph coloring
KW - List-chromatic number (choosability)
KW - The unit-distance graph
UR - http://www.scopus.com/inward/record.url?scp=67349175608&partnerID=8YFLogxK
U2 - 10.1007/s00454-009-9190-2
DO - 10.1007/s00454-009-9190-2
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AN - SCOPUS:67349175608
SN - 0179-5376
VL - 42
SP - 132
EP - 141
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 2
ER -