Chromaticity of a family of K4 homeomorphs Original Research Article

A K4 homeomorph can be described as a graph on n vertices having 4 vertices of degree 3 and n − 4 vertices of degree 2; each pair of degree 3 vertices is joined by a path. We study the chromatic uniqueness and chromatic equivalence of one family of K4 homeomorphs. This family has exactly 3 paths of length one. The results of this study leads us to solve 3 of the problems posed by Koh and Teo in their 1990 survey paper which appeared in Graphs and Combinatorics.