Published October 14, 2026 | Version v1
Working paper Open

A Proof of the Weak Roberson Conjecture

Authors/Creators

  • 1. ROR icon University of Cambridge
  • 2. ROR icon Max Planck Institute for Informatics
  • 3. ROR icon Technical University of Denmark
  • 4. ROR icon RWTH Aachen University
  • 5. ROR icon IT University of Copenhagen

Description

Roberson's weak conjecture asserts that homomorphism indistinguishability over a graph class excluding some minor is never the same as isomorphism. We prove the conjecture in its oddomorphism form: for every $t \geq 1$, there exists an $N$ such that no $K_t$-minor-free graph admits a weak oddomorphism to $K_N$. This implies the conjecture with CFI graphs over complete graphs as separating examples.

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Additional details

Funding

European Commission
CountHom - Counting (with) homomorphisms 101077083

Dates

Submitted
2026-10-14