Finite Bipartite Graphs as Induced Subgraphs of Subfactor Principal Graphs
Manuscript 30 September 2026 · Online 30 September 2026
Abstract
Every finite bipartite simple graph occurs as a vertex-induced unrooted subgraph of the principal graph of an irreducible finite-depth inclusion of hyperfinite type II1 factors. For part sizes m and n, an explicit neighborhood-multiplicity parameter q gives index q3^n, with q at most m+1, and depth at most four. The selected vertices have depths two and three. The complete depth ranks and adjacency spectrum are computed. A separate amplification realizes every finite bipartite multigraph as an ordinary subgraph, with edge deletion allowed.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Finite induced subgraph realization
- Categories
- math.OA · math.CO
- Manuscript
- 30 September 2026
- Online release
- 30 September 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “Finite Bipartite Graphs as Induced Subgraphs of Subfactor Principal Graphs,” EulerSolve Research Papers, AIM-OTHER-0060, 2026. https://doi.org/10.5281/zenodo.23048180.
BibTeX
@misc{Ferudun2026AIMOTHER0060,
author = {Ferudun, Alper},
title = {Finite Bipartite Graphs as Induced Subgraphs of Subfactor Principal Graphs},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/aim-other-0060/},
doi = {10.5281/zenodo.23048180},
note = {AIM-OTHER-0060; unrefereed preprint}
}