The limit of chromatic polynomials
โ Scribed by D Kim; I.G Enting
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 639 KB
- Volume
- 26
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
It is proved that the chromatic polynomial of a connected graph with n vertices and m edges has a root with modulus at least (m&1)ร(n&2); this bound is best possible for trees and 2-trees (only). It is also proved that the chromatic polynomial of a graph with few triangles that is not a forest has a
The chromatic polynomial ;X chromial) of a graph was first defined by Birkhoff in 1912, ;md gives the number of ways or" properly colov iing the vertices of the graph with any number of colours. A good survey of the b-sic facts about these polynomials may be found in the article by Read [ 3 3 . It
## Abstract We prove that the multiplicity of the root 1 in the chromatic polynomial of a simple graph __G__ is equal to the number of nontrivial blocks in __G__. In particular, a connected simple graph __G__ has a cutpoint if and only if its chromatic polynomial is divisible by (ฮป โ 1)^2^. We appl