A sharp-move is known as an unknotting operation for knots. A self sharp-move is a sharp-move on a spatial graph where all strings in the move belong to the same spatial edge. We say that two spatial embeddings of a graph are sharp edge-homotopic if they are transformed into each other by self sharp-moves and ambient isotopies. We investigate how is the sharp edge-homotopy strong and classify all spatial theta curves completely up to sharp edge-homotopy. Moreover we mention a relationship between sharp edge-homotopy and delta edge (resp. vertex)-homotopy on spatial graphs.
@article{urn:eudml:doc:38159, title = {Sharp edge-homotopy on spatial graphs.}, journal = {Revista Matem\'atica de la Universidad Complutense de Madrid}, volume = {18}, year = {2005}, pages = {181-207}, zbl = {1080.57003}, mrnumber = {MR2135538}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38159} }
Nikkuni, Ryo. Sharp edge-homotopy on spatial graphs.. Revista Matemática de la Universidad Complutense de Madrid, Tome 18 (2005) pp. 181-207. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38159/