2-reducible cycles containing three consecutive edges in \((2k+1)\)-edge- connected graphs
The author considers finite undirected multigraphs without loops and allows the repetition of vertices (but not of edges) in a path or cycle. Let \(G\) be a \(k\)-edge-connected graph and let \(f_0\), \(f_1\), \(f_2\) be its consecutive edges. A cycle \(C\) in \(G\) is called 2-reducible if \(G- E(C)\) is \((k- 2)\)-edge-connected. The author finds a nontrivial equivalent reformulation of the condition that no cycle in \(G\) containing \(f_0\), \(f_1\) and \(f_2\) is 2-reducible.
scientific article; zbMATH DE number 784144