Triangle-free CFS graphs (≤12 vertices) and associated RACG data

# 📁 Triangle-Free CFS Graphs ≤ 12 Vertices ### with Right-Angled Coxeter Group (RACG) Invariants This dataset contains **all triangle-free CFS graphs with up to 12 vertices**, together with a variety of geometric, combinatorial, and group-theoretic invariants of the **right-angled Coxeter groups** they define. It supplements the computational and theoretical methods developed in the following preprint: --- ## 📄 Reference Preprint **RAAGedy right-angled Coxeter groups** Christopher H. Cashen, Pallavi Dani, Alexandra Edletzberger, Annette Karrer **arXiv:** 2506.16789 **DOI:** https://doi.org/10.48550/arXiv.2506.16789 **Subjects:** Group Theory (math.GR) **MSC:** 20F65, 20F55 **Length:** 77 pages, 32 figures The dataset complements the arguments in **Sections 4–6** of the preprint, particularly the analysis of:- RAAGedy components and obstructions,- coarse geometric tests for RACG-to-RAAG quasi-isometry,- computational verification for all graphs with ≤10 vertices (extended here to 12). --- ## 📦 Contents CFSdf_up_to_12.pkl ← pandas DataFrame (39 MB)CFS_database_management.py ← lookup and isomorphism utilitiesREADME.md ← this file Each row in the `.pkl` represents **one isomorphism type** of a triangle-free CFS graph with ≤12 vertices. All graphs are already filtered — no extra processing is required. --- ## 🧪 Loading the Dataset ```pythonimport pickle with open("CFSdf_up_to_12.pkl", "rb") as f: data = pickle.load(f) print(len(data), "graphs loaded.")print("Columns:", list(data.columns)) # Example: a square (C₄) — this *is* CFS and appears in the dataset. import networkx as nximport CFS_database_management as cfs G = nx.cycle_graph(4) # 4-cycle C4 try: idx = cfs.dfindex(data, G) print("Found at index:", idx) print(data.loc[idx])except IndexError: print("Unexpected: C4 not found. (Should be present.)") 🧠 Selected DataFrame Columns| Column | Purpose || --------------------------------------------- | ---------------------------------------- || `graph` | NetworkX graph object || `graph_hash` | Degree-based coarse isomorphism hash || `RAAGedy`, `Xi_RAAGedy_component` | RAAGedy classification / component label || `Dani_Levcovitz`, `ZZ_obstruction` | known obstructions from literature || `ladder`, `near_double`, `strong`, `planar` | structural conditions || `stable_cycle_depth`, `compliant_cycle_depth` | depth invariants || `iterated_splittings`, `goc` | splitting and geometric structure || `nodes`, `edges`, `maxvalence` | metadata || `locally_connected_visual_boundary` | RACG boundary property || `totally_disconnected_Morse_boundary` | RACG boundary property | 🔧 Dependenciespip install pandas networkxpip install git+https://github.com/cashenchris/RACG.git Everything needed for lookup and hashing is contained in the single fileCFS_database_management.py. 📌 Dataset Citation (placeholder) When this dataset receives a Zenodo DOI, please cite: Cashen, C. (2025).Triangle-free CFS graphs (≤12 vertices) and associated RACG data (v1.0).Dataset. TU Wien / Zenodo. DOI: TBA 📬 Contact Christopher H. CashenTU WienInstitute of Discrete Mathematics and GeometryWiedner Hauptstraße 8–101040 Vienna, Austria 📧 [e-mail] 🔗 https://github.com/cashenchris