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

Abstract

A graph of order $n>3$ is called {switching separable} if its modulo-2 sum with some complete bipartite graph on the same set of vertices is divided into two mutually independent subgraphs, each having at least two vertices. We prove the following: if removing any one or two vertices of a graph always results in a switching separable subgraph, then the graph itself is switching separable. On the other hand, for every odd order greater than 4, there is a graph that is not switching separable, but removing any vertex always results in a switching separable subgraph. We show a connection with similar facts on the separability of Boolean functions and reducibility of $n$-ary quasigroups. Keywords: two-graph, reducibility, separability, graph switching, Seidel switching, graph connectivity, $n$-ary quasigroup

english: 9 pages; russian: 9 pages

References in corpus (5)

• n-Ary quasigroups of order 4
• On reconstructing reducible n-ary quasigroups and switching subquasigroups
• On irreducible n-ary quasigroups with reducible retracts
• On reducibility of n-ary quasigroups
• On connection between reducibility of an n-ary quasigroup and that of its retracts

Cited by in corpus (1)

• On a test on switching separability of graphs modulo $q$