FIID homomorphisms and entropy inequalities
Endre Csoka, Zoltan Vidnyanszky
TL;DR
This paper explores the limitations of FIID homomorphisms from regular trees to finite graphs, demonstrating that certain graphs with high chromatic number cannot be obtained via such homomorphisms, using entropy inequalities.
Contribution
It introduces entropy inequality techniques to analyze FIID homomorphisms and establishes new non-existence results for high chromatic number graphs.
Findings
No FIID homomorphism exists from a 3-regular tree to graphs with arbitrarily large chromatic number.
Entropy inequalities are effective tools for studying FIID homomorphisms.
Certain complex graphs cannot be represented as FIID homomorphic images of regular trees.
Abstract
We investigate the existence of FIID homomorphisms from regular trees to finite graphs. Using entropy inequalities we show that there are graphs with arbitrarily large chromatic number to which there is no FIID homomorphism from a 3-regular tree.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsOptimization and Variational Analysis · Advanced Optimization Algorithms Research · Functional Equations Stability Results