## Abstract The theorem of Hassler Whitney, which gives the chromatic polynomial of a graph in terms of βbroken circuits,β is used to derive a new formula for the coefficients of chromatic polynomials.
Chromatic polynomials and broken cycles
β Scribed by S.G Hoggar
- Publisher
- Elsevier Science
- Year
- 1975
- Tongue
- English
- Weight
- 705 KB
- Volume
- 19
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this paper we present some results on the sequence of coefficients of the chromatic polynomial of a graph relative to the complete graph basis, that is, when it is expressed as the sum of the chromatic polynomials of complete graphs. These coefficients are the coefficients of what is often called
We prove that, for any pair of integers k, l 1, there exists an integer N(k, l ) such that every graph with chromatic number at least N(k, l ) contains either K k or an induced odd cycle of length at least 5 or an induced cycle of length at least l.
## 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 (Ξ» β 1)^2^. We appl
## Abstract It is proved that all classes of polygon trees are characterized by their chromatic polynomials, and a characterization is given of those polynominals that are chromatic polynomials of outerplanar graphs. The first result yields an alternative proof that outerplanar graphs are recogniza