We prove that if H and H’ are subgraphs of a graph G, and both are isomorphic to subdivisions of K5 or K3, 3, then the following are equivalent: (i) there is a sequence H = H1, H2, ⋯, Hk = H’ of subgraphs of G, each isomorphic to a subdivision of K5 or K3, 3 and each differing only a “small amounty” from its predecessor; (ii) H and H’ are not “separated” in G by a vertex separation of order ≤ 3. This is a lemma for use in a future paper concerning linkless embeddings of graphs in 3-space.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics