We discuss the chromaticity of the graph which consists of a cycle with two crossing chords and give sufficient and necessary condition for it to be chromatically unique.
Chromaticity of a family of K4 homeomorphs
โ Scribed by Zhi-Yi Guo; Earl Glen Whitehead Jr.
- Book ID
- 104113783
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 255 KB
- Volume
- 172
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
โฆ Synopsis
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.
๐ SIMILAR VOLUMES
## Abstract We derive a new formula for the chromatic polynomial of any __K__~4~ homeomorph. We obtain a large family of chromatically unique __K__~4~ homeomorphs. We obtain seven infinite pairs of chromatically equivalent nonisomorphic __K__~4~ homeomorphs.
Chromatic classes of 2-connected (n, n + 2)-graphs which are horneomorphic to K4 and have girth 5 are given in this paper. Lemma 1. (a) If(6,~,rl)ยข Uj~3{(j,j-2,j+ 1), (j-2,j+2,j-1)} andFl (6,~,rl)~ Fl(6t, y',rlt ), then F1(6,7,~/) ~ Ft(6',7',ยข).