We define the IH-complex on the set of spatial trivalent graphs by using the IH-move, which is a local spatial move appeared in a study of knotted handlebodies. The IH-distance between two spatial trivalent graphs is defined by the minimal number of IH-moves needed to transform one into the other. It gives a distance function on the IH-complex. We give a lower bound for the IH-distance, and evaluate it.
"The IH-complex of Spatial Trivalent Graphs." Tokyo J. Math. 33 (2) 523 - 535, December 2010. https://doi.org/10.3836/tjm/1296483486