extend to an isomorphic copy of $\Delta^n$ in $K$. We define a simplicial complex $L$ to be an [*edge-minor*]{} of a simplicial complex $K$ if $L$ is obtained from a subcomplex of $K$ by a sequence of admissible edge contractions.

Yet another equivalent formulation of the admissibility condition is that every point-inverse of $|f|$ is collapsible. This has the following consequences:

1.  If $f{\colon}K\to L$ is an edge contraction, and $\Lambda$ is a subcomplex of $L$, then $f|_{f^{-1}(\Lambda)}$ is either an edge contraction or a homeomorphism.

2.  If $L$ is an edge-minor of $K$ and $|K|$ embeds in $S^m$, then $|L|$ embeds in $S^m$.

E. Nevo considered a slightly different definition of a “minor” which we shall term a [*Nevo minor*]{} [@Ne]. It is similar to that of edge-minor, with the following amendment. We call an edge contraction $f{\colon}K\to L$, where $\dim K=n$, Nevo-admissible, if the $(n-2)$-skeleton $(\operatorname{lk}\{v_1\}\cap\operatorname{lk}\{v_2\})^{(n-2)}=\operatorname{lk}\{v_1,v_2\}$; an equivalent condition is that $\{v_1,v_2\}$ is not contained in any missing face of $K$ of (missing) dimension $\le n$. Note that in the case of graphs this is a vacuous condition.

\[nevo\] The notions of Nevo minor and edge-minor are equivalent.

The author learned from E. Nevo that the published version 