On the Roots of σ‐Polynomials | Zendy

Brown Jason | Zendy; Erey Aysel | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

On the Roots of σ‐Polynomials

Author(s) -

Brown Jason,

Erey Aysel

Publication year - 2016

Publication title -

journal of graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 54

eISSN - 1097-0118

pISSN - 0364-9024

DOI - 10.1002/jgt.21889

Subject(s) - mathematics , combinatorics , chromatic scale , chromatic polynomial , vertex (graph theory) , conjecture , graph , discrete mathematics , order (exchange) , finance , economics

Given a graph G of order n , the σ‐ polynomial of G is the generating function σ ( G , x ) = ∑ a i x iwhere a i is the number of partitions of the vertex set of G into i nonempty independent sets. Such polynomials arise in a natural way from chromatic polynomials. Brenti (Trans Am Math Soc 332 (1992), 729–756) proved that σ‐polynomials of graphs with chromatic number at least n − 2 had all real roots, and conjectured the same held for chromatic number n − 3 . We affirm this conjecture.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research