A note onn-tuple colourings and circular colourings of planar graphs with large odd girth
P. Šparl, Janez Žerovnik · International Journal of Computer Mathematics · 2007
The existence of planar graphs with odd girth 2k+1 and high girth that cannot be (2k+1, k)-coloured was left as an open question by Klostermeyer and Zhang. In this note we show that such graphs exist for arbitrarily large k. We also show that these graphs have fractional chromatic number greater than 2+1/k.