Independent set counts for trees grow with exponent at least 0.1966; planar graphs achieve density one; graphs with linear edge density realize all positive integers via Zaremba's conjecture.
An AI enhanced approach to the tree unimodality conjecture
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
fields
math.CO 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
New counterexamples to log-concavity of dominating-set sequences in trees and graphs are found via AI search, with a construction giving arbitrarily many violations and positive log-concavity results for caterpillar graphs and a continuous analogue.
citing papers explorer
-
Independent Sets and Continued Fractions
Independent set counts for trees grow with exponent at least 0.1966; planar graphs achieve density one; graphs with linear edge density realize all positive integers via Zaremba's conjecture.
-
Trees and Graphs with Non Log-concave Dominating Set Sequence via AI Tools
New counterexamples to log-concavity of dominating-set sequences in trees and graphs are found via AI search, with a construction giving arbitrarily many violations and positive log-concavity results for caterpillar graphs and a continuous analogue.