Geodesic
On a~connection between the switching separability of a~graph and of its subgraphs
Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 2, pp. 46-56

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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.
Keywords: graph connectivity, graph switching, $n$-ary quasigroups, reducibility, Seidel switching, separability, two-graphs. 
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     author = {D. S. Krotov},
     title = {On a~connection between the switching separability of a~graph and of its subgraphs},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {46--56},
     publisher = {mathdoc},
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     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2010_17_2_a3/}
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D. S. Krotov. On a~connection between the switching separability of a~graph and of its subgraphs. Diskretnyj analiz i issledovanie operacij, Tome 17 (2010) no. 2, pp. 46-56. http://geodesic.mathdoc.fr/item/DA_2010_17_2_a3/