Multiple breaks of log-concavity in the independence polynomials of trees

2025/11/01 by César Bautista-Ramos, Bautista-Ramos, César
Mathematics · #Advanced Combinatorial Mathematics #Graph theory and applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2511.00334

Abstract

We construct infinite families of trees whose independence polynomials violate log-concavity at an arbitrary number of indices. This affirmatively answers a question of D. Galvin.

Citations

• An AI enhanced approach to the tree unimodality conjecture
• Trees with non log-concave independent set sequences
• The independence polynomial of trees is not always log-concave starting from order 26
• Very well-covered graphs with log-concave independence polynomials

Related

• The independence polynomial of trees is not always log-concave starting from order 26
• Trees with non log-concave independent set sequences
• A symmetric function approach to log-concavity of independence polynomials
• On Unimodality of Independence Polynomials of Trees
• Very well-covered graphs with log-concave independence polynomials