Chromatic uniqueness and equivalence of K4 homeomorphs
โ Scribed by Earl Glen Whitehead Jr.; Lian-Chang Zhao
- Book ID
- 102343819
- Publisher
- John Wiley and Sons
- Year
- 1984
- Tongue
- English
- Weight
- 330 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
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.
๐ SIMILAR VOLUMES
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
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.
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).