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research article

Lorentzian polynomials and the independence sequences of graphs

Bendjeddou, Amire  
•
Hardiman, Leonard  
February 25, 2025
Bulletin Of The London Mathematical Society

We study the multivariate independence polynomials of graphs and the log-concavity of the coefficients of their univariate restrictions. Let R-W4 be the operator defined on simple and undirected graphs which replaces each edge with a caterpillar of size 4. We prove that all graphs in the image of R-W4 are what we call pre-Lorentzian, that is, their multivariate independence polynomial becomes Lorentzian after appropriate manipulations. In particular, as pre-Lorentzian graphs have log-concave (and therefore unimodal) independence sequences, our result makes progress on a conjecture of Alavi, Malde, Schwenk and Erd & odblac;s which asks if the independence sequence of trees or forests is unimodal.

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Type
research article
DOI
10.1112/blms.70031
Web of Science ID

WOS:001430689100001

Author(s)
Bendjeddou, Amire  
•
Hardiman, Leonard  
Date Issued

2025-02-25

Publisher

WILEY

Published in
Bulletin Of The London Mathematical Society
Subjects

UNIMODALITY

•

FAMILIES

•

TREES

•

Science & Technology

•

Physical Sciences

Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
CSFT  
AVP-E-CMS  
Available on Infoscience
March 7, 2025
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/247585
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