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Chromatic uniqueness and equivalence of K4 homeomorphs

โœ 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

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โœฆ 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.


๐Ÿ“œ SIMILAR VOLUMES


Chromaticity of a family of K4 homeomorp
โœ Zhi-Yi Guo; Earl Glen Whitehead Jr. ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 255 KB

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-homeomorp
โœ Shaoji Xu ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 228 KB

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 certain 2-connected
โœ X.E. Chen; K.Z. Ouyang ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 445 KB

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).