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On the Location of Roots of Independence Polynomials

✍ Scribed by J.I. Brown; C.A. Hickman; R.J. Nowakowski


Book ID
111587722
Publisher
Springer
Year
2004
Tongue
English
Weight
88 KB
Volume
19
Category
Article
ISSN
0925-9899

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On the Roots of Chromatic Polynomials
✍ Jason I. Brown πŸ“‚ Article πŸ“… 1998 πŸ› Elsevier Science 🌐 English βš– 158 KB

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)Γ‚(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