Abstract :
Let K4(a,b,c,d,e,f) denote the K4 homeomorph in which the lengths of its six paths between pairs of degree-3 vertices are a,b,c,d,e,f, respectively. In this paper, we study the chromatic uniqueness and chromatic equivalence of K4(a,b,c,d,e,f) when exactly three of a,b,c,d,e,f are equal to s(⩾2).