2023/09/02 by Johannes Carmesin, Carmesin, Johannes, Jan Kurkofka +1 · 1 citation
Computer Science · #05C05 #05C10 (Secondary) #05C40 #05C83 (Primary) #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.2309.00902
openalex publication_date 2023/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Every large k-connected graph-minor induces a k-tangle in its ambient graph. The converse holds for k≤ 3, but fails for k≥ 4. This raises the question whether `k-connected' can be relaxed to obtain a characterisation of k-tangles through highly cohesive graph-minors. We show that this can be achieved for k=4 by proving that internally 4-connected graphs have unique 4-tangles, and that every graph with a 4-tangle τ has an internally 4-connected minor whose unique 4-tangle lifts to τ.