Pairs Of Edges As Chords And As Cut-Edges

Several BLACK WALNUT COMPLETE authors have studied the graphs for which every edge is a chord of a cycle; among 2-connected graphs, one characterization is that the deletion of one vertex never creates a cut-edge.Two new results: among 3-connected graphs with minimum degree at least 4, every two adjacent edges are Eyewear chords of a common cycle if and only if deleting two vertices never creates two adjacent cut-edges; among 4-connected graphs, every two edges are always chords of a common cycle.