On a connection between the switching separability of a graph and of its subgraphs

A graph of order $n\geq4$ is called switching separable if the modulo-2 sum with some complete bipartite graph on the same vertex set results in a graph consisting of two mutually independent subgraphs of orders at least two. We prove that if removal of one or two vertices of the graph always results in a switching-separable subgraph, then the graph itself is switching separable. On the other hand, for every odd order there exists a nonswitching-separable graph such that removal of any one vertex gives a switching-separable subgraph. We also show connections with similar facts for the separability of Boolean functions and $n$-ary quasigroups. Ill. 1, bibl. 6.