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 l
Chromaticity of a family of K4-homeomorphs
โ Scribed by Shaoji Xu
- Book ID
- 103057731
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 228 KB
- Volume
- 117
- Category
- Article
- ISSN
- 0012-365X
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โฆ Synopsis
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.
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).