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
On Quadratic Relations between Roots of Polynomials
โ Scribed by Kurt Girstmair
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 134 KB
- Volume
- 188
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let = be a fundamental unit in a real quadratic field and let S be the set of rational primes p for which = has maximal order modulo p. Under the assumption of the generalized Riemann hypothesis, we show that S has a density $(S)=c } A in the set of all rational primes, where A is Artin's constant a
An explicit criterion for the determination of the numbers and multiplicities of the real/imaginary roots for polynomials with symbolic coefficients is based on a Complete Discrimination System (CDS). A CDS is a set of explicit expressions in terms of the coefficients that are sufficient for determi
We confirm a conjecture of L. Merel (H. Darmon and L. Merel, J. Reine Angew. Math. 490 (1997), 81-100) describing a certain relation between the jacobians of various quotients of X p in terms of specific correspondences. The method of proof involves reducing this conjecture to a question about certa