On the chromatic uniqueness of $K_4$-homeomorphs with girth 7

Abstract

This paper settled the question, which remains open in article published in Discrete Mathematics in 2008. Graphs homeomorphic to $K_4$, i.e., cliques on 4 vertices with edges replaced by paths are considered in this work. This work completes the study of chromaticity of $K_4$-homeomorphs of girth 7.

13 pages