We improve an upper bound for the chromatic index of a multigraph due to Andersen and Gol'dberg. As a corollary w e deduce that if no t w o edges of multiplicity at least t w o in G are adjacent, then ,y'(G) s A ( G ) + 1. In addition w e generalize results concerning the structure of critical graph
A note concerning chromatic polynomials
β Scribed by Chong-Yun Chao; Lian-Chang Zhao
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 180 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The chromatic polynomials of certain families of graphs can be expressed in terms of the eigenspaces of a linear operator. The operator is represented by a matrix, which is referred to here as the compatibility matrix. In this paper complete sets of eigenfunctions are obtained for several related fa
Woodall, D.R., A zero-free interval for chromatic polynomials, Discrete Mathematics 101 (1992) 333-341. It is proved that, for a wide class of near-triangulations of the plane, the chromatic polynomial has no zeros between 2 and 2.5. Together with a previously known result, this shows that the zero
Let P(G, \*) denote the chromatic polynomial of a graph G. It is proved in this paper that for every connected graph G of order n and real number \* n, (\*&2) n&1 P(G, \*)&\*(\*&1) n&2 P(G, \*&1) 0. By this result, the following conjecture proposed by Bartels and Welsh is proved: P(G, n)(P(G, n&1))
## 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.