The Enumeration of Point Labelled Chromatic Graphs and Trees

Abstract

Given n points with c₁ of one colour, c₂ of another colour, up to k colours, linear graphs are formed with the restriction that no line connects points of the same colour. Following fairly standard terminology, coloured graphs with this restriction will be called point chromatic graphs. Giving the points numerical labels running from 1 to c_i for points of the ith colour (i = 1, 2, … , k) forms point labelled chromatic graphs. Note that this description is slightly different from assigning a label and a colour independently to each point.