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Spatial-graph isotopy for trivalent graphs and minimally knotted embeddings. (English) Zbl 0861.57005

Summary: We study spatial-graph isotopy for trivalent graphs, and give a connection between this equivalence relation and minimally knotted embeddings of graphs into 3-space. It will be seen that a rearrangement theorem (Theorem 2) plays an important role in investigating mutually isotopic embeddings of a trivalent graph.

MSC:

57M15 Relations of low-dimensional topology with graph theory
57M25 Knots and links in the \(3\)-sphere (MSC2010)
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