Eulerian subgraphs and \(S\)-connectivity of graphs (Q2185427)

A graph \(G\) is collapsible if for any vertex subset \(X\) of \(G\) of even order, there exists a connected spanning subgraph of \(G\) whose vertices have degree exactly odd in \(X\) and even otherwise. The authors prove that collapsible graphs are \(S\)-connected for all abelian groups \(S\) of even order and for all abelian groups of odd order when \(|S| \geq 53\).