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Christoffel–Darboux Type Identities for the Independence Polynomial

Published online by Cambridge University Press:  02 April 2018

FERENC BENCS
FERENC BENCS*
Affiliation:
Eötvös Loránd Tudományegyetem, H-1117 Budapest, Pázmány Péter sétány 1/C, Hungary Central European University, H-1051 Budapest, Nador utca 9, Hungary (e-mail: bencs.ferenc@renyi.mta.hu)
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Abstract

In this paper we introduce some Christoffel–Darboux type identities for independence polynomials. As an application, we give a new proof of a theorem of Chudnovsky and Seymour, which states that the independence polynomial of a claw-free graph has only real roots. Another application is related to a conjecture of Merrifield and Simmons.

Keywords

Primary 05C31Secondary 05A1905C30

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 27 , Issue 5 , September 2018 , pp. 716 - 724
Copyright
Copyright © Cambridge University Press 2018 

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References

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