Colourings with Bounded Monochromatic Components in Graphs of Given Circumference [article]

Bojan Mohar and Bruce Reed and David R. Wood
2017 arXiv   pre-print
We prove that every graph with circumference at most k is O( k)-colourable such that every monochromatic component has size at most O(k). The O( k) bound on the number of colours is best possible, even in the setting of colourings with bounded monochromatic degree.
arXiv:1612.05674v2 fatcat:b2kbmprb2rhxnmycq7wmodeuoy