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Trees and Graphs with Non Log-concave Dominating Set Sequence via AI Tools

Year: 2026

Type: preprint

Abstract: We give new examples of graphs and trees with dominating set sequences that are not log-concave. These examples were generated by PatternBoost, a transformer-based reinforcement learning software developed by Charton-Ellenberg-Wagner-Williamson. We also show: for any positive integer $m$, there exists a tree whose dominating set sequence is not log-concave for at least $m$ indices by modifying a similar construction of Bautista-Ramos for the independent set sequence. We show that a large class of caterpillar graphs has log-concave dominating set sequences. A continuous analogue of the sequence is also log-concave for all graphs.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2605.02193

Authors: Du, Alina, Heilman, Steven, Panova, Greta

Institution: University of Southern California

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Collaborative Research: AF: Small: Computational Complexity and Algebraic Combinatorics, AF: Small: Graph Cut Complexity, Weak Unique Games, and Adam Nonconvergence

OpenAlex ID: W7160295281

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