Work

Schrijver-Delsarte rigidity in association schemes and undecidability of quantum graph homomorphism

Year: 2026

Type: preprint

Abstract: We prove RE-completeness of the quantum homomorphism problem parameterised by families of graphs derived from the classic metric association schemes. These include Kneser graphs, $q$-Kneser graphs, and the complements of Johnson, Grassmann, and Hamming graphs. Our proof develops a spectral method for establishing non-contextuality of quantum polymorphisms. It combines an equality analysis of Roberson's bound on the projective packing number in terms of Schrijver's theta with a structural argument inspired by Erdős-Ko-Rado theory.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.20678

Authors: Ciardo, Lorenzo, Hebbeker, Iris, Joubert, Gideo, Kreiß, Jana, Mottet, Antoine

Institutions: Hamburg University of Technology, Graz University of Technology

Language: English

Topic: Advanced Graph Theory Research

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, European Regional Development Fund

OpenAlex ID: W7213596284

Cites: 13

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Related to: 10