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On the cost of computing roots of polynomials

✍ Scribed by Harold W. Kuhn; Zeke Wang; Senlin Xu

Book ID
110590081
Publisher
Springer-Verlag
Year
1984
Tongue
English
Weight
367 KB
Volume
28
Category
Article
ISSN
0025-5610

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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