Minimally knotted spatial graphs are totally knotted (Q1429091)

A knotted spatial planar graph is said to be minimally knotted if all of its spatial proper subgraphs are unknotted. It is known that any planar graph admits a minimally knotted spatial graph [\textit{A. Kawauchi}, Osaka J. Math. 26, 743--758 (1989; Zbl 0701.57015)], [\textit{Y.-Q. Wu}, Math. Z. 214, 653--658 (1993; Zbl 0789.57006)]. A spatial graph is said to be totally knotted if the exterior of the graph is irreducible and \(\partial\)-irreducible. In this paper the authors prove that any minimally knotted spatial connected planar graph is totally knotted by techniques of three-dimensional topology.