Point partition numbers and girth
Roger J. Cook · Proceedings of the American Mathematical Society · 1975
In recent papers D. R. Lick and A. T. White have introduced point partition numbers as generalizations of the chromatic number and the point-arboricity of a graph. In particular they proved that an analogue of Heawood’s theorem holds for the point partition numbers. In the present paper it is shown that the bounds provided by their result may be improved for graphs of large girth. Finally, using a method of Erdös, it is shown that there exist graphs with large girth and large point-partition number.