Every cubic cage is quasi 4-connected (Q1810654)

A \((\delta, g)\)-cage is a regular graph of degree \(\delta\) and girth \(g\) with the least possible number of vertices. In the cited literature it has been proved that every \((3,g)\)-cage is 3-connected and it has been conjectured that all \((\delta, g)\)-cages are \(\delta\)-connected for every \(\delta\geq 3\). The authors further study this hypothesis and prove that every \((3,g)\)-cage with \(g\geq 5\) is quasi 4-connected.